From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

The study of neuronal interactions is at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, and the Brainome) that attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott (2006), we extend them to heavy-tailed distributions of interactions. More important, we analytically derive the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that on imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong nonorthogonality of associated eigenvectors. This leads us to the conclusion that understanding the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.

Development of a bedside scoring system for predicting a first recurrence of Clostridium difficile-associated diarrhea

PURPOSE

A scoring system for identifying patients at high or low risk for recurrent Clostridium difficile-associated diarrhea (CDAD) is described.

METHODS

A retrospective cohort study was performed using data on adults with CDAD admitted to a 3-hospital system from 2009 to 2014. The primary endpoint was the rate of recurrent CDAD within 60 days of clinical cure of CDAD. Risk factors for CDAD recurrence were identified, and a risk prediction tool was developed using multivariate logistic regression.

RESULTS

The CDAD cure rate in the study cohort (n = 340) was 92.3%; the 60-day recurrence rate was 16.9%. Five factors were significantly associated with high recurrence risk: presence of CDAD at admission, body temperature of >37.8 °C at admission, leukocytosis, nosocomial CDAD, and abdominal distention on CDAD presentation. From that information a risk prediction tool, the CDAD "recurrence score," was developed (1 point is assigned for each factor present, for a maximum score of 5). Validation testing of the recurrence score indicated an area under the receiver operating characteristic curve of 0.72 (95% confidence interval, 0.65-0.80). A score of ≥2 had a negative predictive value of 91%, while a score of ≥4 had a positive predictive value of 70%.

CONCLUSION

If externally validated in future studies, a tool for predicting the risk of recurrent CDAD using data readily available at the time of presentation could allow clinicians to identify patients at high risk for recurrence, address modifiable risk factors, and select tailored treatments to improve patient outcomes.

A novel case of NKX3.1-positive metastatic cutaneous prostate cancer

Prostate carcinoma is the most common non-dermatological malignancy in men and only second to lung cancer as the leading cause of cancer related deaths in America. Moreover, metastasis to the skin is even more uncommon following apparently successful treatment of a preexisting prostate cancer. We present an 87-year-old man previously diagnosed with prostate cancer treated with brachytherapy, who presented with a metastatic prostate adenocarcinoma of the scalp mimicking a basal cell carcinoma. Herein, we present a patient with an NKX 3.1 positive cutaneous metastatic prostate carcinoma identified through NKX3.1 stain rather than the typical PSA/PSAP stain.

A case of leprosy in central Florida

Hansen disease, also known as leprosy, is a chronic granulomatous infectious disease that is caused by Mycobacterium leprae. We report an unusual case of a 65-year-old man who presented with multiple anesthetic, annular, erythematous, scaly plaques with a raised border without any known exposures to leprosy. Histologic examination revealed a perineural lymphohistiocytic infiltrate and rare bacilli demonstrated on Fite staining. After confirmation with polymerase chain reaction (PCR) and consultation with the National Hansen's Disease Program (Baton Rouge, Louisiana), the patient was placed on a regimen of rifampicin 600 mg once monthly and dapsone 100 mg once daily for 6 months, which showed considerable improvement. This case demonstrates the identification of leprosy in central Florida, a region that is not known to be endemic to the disease. Leprosy, however rare, must be part of a practitioner's differential diagnosis even without history of traditional exposures.

Evolutionary games on cycles with strong selection

Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.

Prolonged oral antibiotic suppression in osteomyelitis and associated outcomes in a Veterans population

OBJECTIVE

Prolonged oral antimicrobial suppression has been suggested as an alternative treatment for patients with prosthetic joint infections who are unable or unwilling to undergo surgical intervention; however, little data exists for utilizing this approach in patients with chronic osteomyelitis and no artificial hardware.

METHODS

We retrospectively reviewed the medical records of all patients over a 5-year time frame who were treated with chronic oral antibiotic suppression for osteomyelitis and who had no artificial hardware. Clinical outcomes, risk factors for treatment failure, and adverse drug reactions were evaluated.

RESULTS

A total of 20 patients were included for evaluation, of which 12 (60%) were able to achieve successful suppression of disease for a mean duration of 778 ± 408 days after discontinuation. Diabetic patients were found to be at higher risk for treatment failure (p = 0.0281). We also identified a high rate of adverse events (25%) attributable to suppressive medications. Despite elevated inflammatory markers contributing to the decision to initiate antibiotic suppression in the majority of patients, few were able to achieve normal values throughout suppressive therapy.

CONCLUSION

Further randomized, controlled studies are needed to determine the utility of antibiotic suppression. However, prolonged oral antibiotic suppression may be a reasonable last-line treatment alternative for chronic osteomyelitis, even in the absence of artificial hardware, for patients who are unwilling or unable to undergo optimal surgical intervention.

Spatial evolution of tumors with successive driver mutations

We study the influence of driver mutations on the spatial evolutionary dynamics of solid tumors. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of cancer clones is deterministic, while mutants arise stochastically.

Incidence of Circulating Antibodies Against Hemagglutinin of Influenza Viruses in the Epidemic Season 2013/2014 in Poland

The aim of this study was to determine the level of antibodies against hemagglutinin of influenza viruses in the sera of people in different age groups in the epidemic season 2013/2014 in Poland. The level of anti-hemagglutinin antibodies was determined by hemagglutination inhibition test (HAI). A total number of 1,050 randomly selected sera was tested in seven age groups. The level of antibodies against influenza viruses was very low, which indicates that the people have not been vaccinated against influenza in the epidemic season 2013/2014. The value of protection rate against influenza in the Polish population is very low. These results are worrying, because complications of influenza may be harmful to health and even life-threatening to persons who are not vaccinated. Furthermore, these results confirm the circulation of three antigenically different influenza virus strains, two subtypes of influenza A virus – A/California/7/2009/(H1N1)pdm09 and A/Victoria/361/2011(H3N2) - and B/Massachusetts/2/2012.

Dissecting x-ray-emitting gas around the center of our galaxy

Most supermassive black holes (SMBHs) are accreting at very low levels and are difficult to distinguish from the galaxy centers where they reside. Our own Galaxy's SMBH provides an instructive exception, and we present a close-up view of its quiescent x-ray emission based on 3 megaseconds of Chandra observations. Although the x-ray emission is elongated and aligns well with a surrounding disk of massive stars, we can rule out a concentration of low-mass coronally active stars as the origin of the emission on the basis of the lack of predicted iron (Fe) Kα emission. The extremely weak hydrogen (H)-like Fe Kα line further suggests the presence of an outflow from the accretion flow onto the SMBH. These results provide important constraints for models of the prevalent radiatively inefficient accretion state.

Clinical and economic outcomes of a prospective antimicrobial stewardship program

PURPOSE

A pre-post analysis of an antimicrobial stewardship program (ASP) involving the use of data-mining software to prospectively identify cases for ASP intervention was conducted.

METHODS

The investigators evaluated clinical outcomes and cost metrics before and after implementation of the ASP, which entailed daily physician review of summary reports on all adult inpatients receiving antimicrobial therapy. The primary outcome measures were annual antimicrobial expenditures and rates of infections due to common nosocomial pathogens; secondary outcome measures included patient survival and length of stay (LOS) in cases involving the indicator diagnoses of pneumonia and abdominal sepsis.

RESULTS

Antimicrobial expenditures, which had increased by an average of 14.4% annually in the years preceding ASP implementation, decreased by 9.75% in the first year of the program and remained relatively stable in subsequent years, with overall cumulative cost savings estimated at $1.7 million. Rates of nosocomial infections involving Clostridium difficile, methicillin-resistant Staphylococcus aureus, and vancomycin-resistant enterococci all decreased after ASP implementation. A pre-post comparison of survival and LOS in patients with pneumonia (n = 2186) or abdominal sepsis (n = 225) showed no significant differences in those outcomes in either patient group, possibly due to the hospital's initiation of other, concurrent infection-control programs during the study period.

CONCLUSION

A prospective collaborative ASP employed automated reports to efficiently identify key data for ASP review. After ASP implementation, antimicrobial expenditures and rates of nosocomial infections caused by resistant pathogens dropped without significant changes in patient survival, LOS, and readmissions for the two studied illness categories.

Spectral relations between products and powers of isotropic random matrices

We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble is equal to the eigenvalue density of nth power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation, one can derive the limiting density of the product of n independent identically distributed non-Hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also provide evidence that the result holds also for isotropic orthogonal ensembles.

Multiplication law and S transform for non-Hermitian random matrices

We derive a multiplication law for free non-Hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define the corresponding non-Hermitian S transform being a natural generalization of the Voiculescu S transform. In addition, we extend the classical Hermitian S transform approach to deal with the situation when the random matrix ensemble factors have vanishing mean including the case when both of them are centered. We use planar diagrammatic techniques to derive these results.

Eigenvalues and singular values of products of rectangular gaussian random matrices

We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular gaussian random matrices in the limit of large matrix dimensions. We show that they both have power-law behavior at zero and determine the corresponding powers. We also propose a heuristic form of finite size corrections to these expressions which very well approximates the distributions for matrices of finite dimensions.

Engagement and retention: measuring breadth and depth of participant use of an online intervention

BACKGROUND

The Internet provides us with tools (user metrics or paradata) to evaluate how users interact with online interventions. Analysis of these paradata can lead to design improvements.

OBJECTIVE

The objective was to explore the qualities of online participant engagement in an online intervention. We analyzed the paradata in a randomized controlled trial of alternative versions of an online intervention designed to promote consumption of fruit and vegetables.

METHODS

Volunteers were randomized to 1 of 3 study arms involving several online sessions. We created 2 indirect measures of breadth and depth to measure different dimensions and dynamics of program engagement based on factor analysis of paradata measures of Web pages visited and time spent online with the intervention materials. Multiple regression was used to assess influence of engagement on retention and change in dietary intake.

RESULTS

Baseline surveys were completed by 2513 enrolled participants. Of these, 86.3% (n = 2168) completed the follow-up surveys at 3 months, 79.6% (n = 2027) at 6 months, and 79.4% (n = 1995) at 12 months. The 2 tailored intervention arms exhibited significantly more engagement than the untailored arm (P < .01). Breadth and depth measures of engagement were significantly associated with completion of follow-up surveys (odds ratios [OR] = 4.11 and 2.12, respectively, both P values < .001). The breadth measure of engagement was also significantly positively associated with a key study outcome, the mean increase in fruit and vegetable consumption (P < .001).

CONCLUSIONS

By exploring participants' exposures to online interventions, paradata are valuable in explaining the effects of tailoring in increasing participant engagement in the intervention. Controlling for intervention arm, greater engagement is also associated with retention of participants and positive change in a key outcome of the intervention, dietary change. This paper demonstrates the utility of paradata capture and analysis for evaluating online health interventions.

TRIAL REGISTRATION

NCT00169312; http://clinicaltrials.gov/ct2/show/NCT00169312 (Archived by WebCite at http://www.webcitation.org/5u8sSr0Ty).

Wealth condensation in pareto macroeconomies

We discuss a Pareto macroeconomy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth, and compare our results to a similar analysis in a super-open system (c) with unbounded wealth [J.-P. Bouchaud and M. Mézard, Physica A 282, 536 (2000)]. Wealth condensation takes place in the social phase for closed and open economies, while it occurs in the liberal phase for super-open economies. In the first two cases, the condensation is related to a mechanism known from the balls-in-boxes model, while in the last case, to the nonintegrable tails of the Pareto distribution. For a closed macroeconomy in the social phase, we point to the emergence of a "corruption" phenomenon: a sizeable fraction of the total wealth is always amassed by a single individual.

Role of CD8(+) lymphocytes in control of simian immunodeficiency virus infection and resistance to rechallenge after transient early antiretroviral treatment

Transient antiretroviral treatment with tenofovir, (R)-9-(2-phosphonylmethoxypropyl)adenine, begun shortly after inoculation of rhesus macaques with the highly pathogenic simian immunodeficiency virus (SIV) isolate SIVsmE660, facilitated the development of SIV-specific lymphoproliferative responses and sustained effective control of the infection following drug discontinuation. Animals that controlled plasma viremia following transient postinoculation treatment showed substantial resistance to subsequent intravenous rechallenge with homologous (SIVsmE660) and highly heterologous (SIVmac239) SIV isolates, up to more than 1 year later, despite the absence of measurable neutralizing antibody. In some instances, resistance to rechallenge was observed despite the absence of detectable SIV-specific binding antibody and in the face of SIV lymphoproliferative responses that were low or undetectable at the time of challenge. In vivo monoclonal antibody depletion experiments demonstrated a critical role for CD8(+) lymphocytes in the control of viral replication; plasma viremia rose by as much as five log units after depletion of CD8(+) cells and returned to predepletion levels (as low as <100 copy Eq/ml) as circulating CD8(+) cells were restored. The extent of host control of replication of highly pathogenic SIV strains and the level of resistance to heterologous rechallenge achieved following transient postinoculation treatment compared favorably to the results seen after SIVsmE660 and SIVmac239 challenge with many vaccine strategies. This impressive control of viral replication was observed despite comparatively modest measured immune responses, less than those often achieved with vaccination regimens. The results help establish the underlying feasibility of efforts to develop vaccines for the prevention of AIDS, although the exact nature of the protective host responses involved remains to be elucidated.

Reward and punishment

Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This result holds in particular for the well-known Ultimatum Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution of economically productive behavior, with agents contributing to the public good and either punishing those who do not or rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably more effective with punishment than with reward.

Natural selection of the critical period for language acquisition

The language acquisition period in humans lasts about 13 years. After puberty it becomes increasingly difficult to learn a language. We explain this phenomenon by using an evolutionary framework. We present a dynamical system describing competition between language acquisition devices, which differ in the length of the learning period. There are two selective forces that play a role in determining the critical learning period: (i) having a longer learning period increases the accuracy of language acquisition; (ii) learning is associated with certain costs that affect fitness. As a result, there exists a limited learning period which is evolutionarily stable. This result is obtained analytically by means of a Nash equilibrium analysis of language acquisition devices. Interestingly, the evolutionarily stable learning period does not maximize the average fitness of the population.

Cytotoxic T-cell abundance and virus load in human immunodeficiency virus type 1 and human T-cell leukaemia virus type 1

The correlation between virus load and specific cytotoxic T-lymphocyte (CTL) frequency during the chronic phase in human immunodeficiency virus type 1 (HIV-1) infection has been found to be negative in cross-sectional studies. We report here that, in infection with the related retrovirus human T-cell leukaemia virus type 1 (HTLV-1), the correlation is positive in asymptomatic carriers and zero in patients with the associated inflammatory disease HTLV-1-associated myelopathy/tropical spastic paraparesis (HAM/TSP). We demonstrate that the direction of the correlation may depend on the efficacy of the CTL response using mathematical models. We conclude that the CTL response is effective in asymptomatic carriers of HTLV-1, but ineffective in patients with HAM/TSP. Virus-mediated impairment of specific CTL production in HIV-1 infection can account for the negative correlation observed.

The evolutionary dynamics of the lexical matrix

The lexical matrix is an integral part of the human language system. It provides the link between word form and word meaning. A simple lexical matrix is also at the center of any animal communication system, where it defines the associations between form and meaning of animal signals. We study the evolution and population dynamics of the lexical matrix. We assume that children learn the lexical matrix of their parents. This learning process is subject to mistakes: (i) children may not acquire all lexical items of their parents (incomplete learning); and (ii) children might acquire associations between word forms and word meanings that differ from their parents' lexical items (incorrect learning). We derive an analytic framework that deals with incomplete learning. We calculate the maximum error rate that is compatible with a population maintaining a coherent lexical matrix of a given size. We calculate the equilibrium distribution of the number of lexical items known to individuals. Our analytic investigations are supplemented by numerical simulations that describe both incomplete and incorrect learning, and other extensions.

A generalized adaptive dynamics framework can describe the evolutionary Ultimatum Game

Adaptive dynamics describes the evolution of games where the strategies are continuous functions of some parameters. The standard adaptive dynamics framework assumes that the population is homogeneous at any one time. Differential equations point to the direction of the mutant that has maximum payoff against the resident population. The population then moves towards this mutant. The standard adaptive dynamics formulation cannot deal with games in which the payoff is not differentiable. Here we present a generalized framework which can. We assume that the population is not homogeneous but distributed around an average strategy. This approach can describe the long-term dynamics of the Ultimatum Game and also explain the evolution of fairness in a one-parameter Ultimatum Game.

The evolutionary dynamics of grammar acquisition

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the grammar of their native language without formal education simply by hearing a number of sample sentences. Children could not solve this learning task if they did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited set of candidate grammars. The restricted search space and the mechanism which allows to evaluate the sample sentences is called universal grammar. Universal grammar cannot be learned; it must be in place when the learning process starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning. We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance for which a predominant grammar is stable. We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar.

Evolution of universal grammar

Universal grammar specifies the mechanism of language acquisition. It determines the range of grammatical hypothesis that children entertain during language learning and the procedure they use for evaluating input sentences. How universal grammar arose is a major challenge for evolutionary biology. We present a mathematical framework for the evolutionary dynamics of grammar learning. The central result is a coherence threshold, which specifies the condition for a universal grammar to induce coherent communication within a population. We study selection of grammars within the same universal grammar and competition between different universal grammars. We calculate the condition under which natural selection favors the emergence of rule-based, generative grammars that underlie complex language.

Evolutionary biology of language

Language is the most important evolutionary invention of the last few million years. It was an adaptation that helped our species to exchange information, make plans, express new ideas and totally change the appearance of the planet. How human language evolved from animal communication is one of the most challenging questions for evolutionary biology The aim of this paper is to outline the major principles that guided language evolution in terms of mathematical models of evolutionary dynamics and game theory. I will discuss how natural selection can lead to the emergence of arbitrary signs, the formation of words and syntactic communication.

The spatial ultimatum game

In the ultimatum game, two players are asked to split a certain sum of money. The proposer has to make an offer. If the responder accepts the offer, the money will be shared accordingly. If the responder rejects the offer, both players receive nothing. The rational solution is for the proposer to offer the smallest possible share, and for the responder to accept it. Human players, in contrast, usually prefer fair splits. In this paper, we use evolutionary game theory to analyse the ultimatum game. We first show that in a non-spatial setting, natural selection chooses the unfair, rational solution. In a spatial setting, however, much fairer outcomes evolve.

Immunological transitions in response to antigenic mutation during viral infection

Antigenic variation is an important factor in viral persistence and disease progression. We analyze immunological changes which occur in response to antigenic mutation during chronic viral infection. Using an established model of viral and immune system dynamics, we determine which qualitative shifts in the immune response can be elicited by the appearance of a new mutant. We find that antigenic mutation can cause dramatic shifts in the magnitude and type of anti-viral immune response. For example, the appearance of a mutant can elicit a new immune response which recognizes the original viral strain. We also find that novel strains of the virus which replicate more slowly than existing viral strains are able to invade and survive, even when the immune system is capable of mounting an immune response against the mutant.

Predicting species diversity in tropical forests

A fundamental question in ecology is how many species occur within a given area. Despite the complexity and diversity of different ecosystems, there exists a surprisingly simple, approximate answer: the number of species is proportional to the size of the area raised to some exponent. The exponent often turns out to be roughly 1/4. This power law can be derived from assumptions about the relative abundances of species or from notions of self-similarity. Here we analyze the largest existing data set of location-mapped species: over one million, individually identified trees from five tropical forests on three continents. Although the power law is a reasonable, zeroth-order approximation of our data, we find consistent deviations from it on all spatial scales. Furthermore, tropical forests are not self-similar at areas Collapse

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Fairness versus reason in the ultimatum game

In the Ultimatum Game, two players are offered a chance to win a certain sum of money. All they must do is divide it. The proposer suggests how to split the sum. The responder can accept or reject the deal. If the deal is rejected, neither player gets anything. The rational solution, suggested by game theory, is for the proposer to offer the smallest possible share and for the responder to accept it. If humans play the game, however, the most frequent outcome is a fair share. In this paper, we develop an evolutionary approach to the Ultimatum Game. We show that fairness will evolve if the proposer can obtain some information on what deals the responder has accepted in the past. Hence, the evolution of fairness, similarly to the evolution of cooperation, is linked to reputation.

CD8 memory, immunodominance, and antigenic escape

Previous theoretical work has suggested that efficient virus control or clearance requires antigen-independent persistence of memory cytotoxic T lymphocyte precursors (CTLp), and that failure to generate such memory CTLp can result in persistent infection and eventual loss of virus control. Here we use mathematical models to investigate the relationship between virus control, the clonal composition of the CTL response and the chance of the virus to evolve antigenic escape. In the presence of efficient memory CTLp, virus is controlled at very low levels by a broad CTL response directed against multiple epitopes. In this case, antigenic escape of the virus population is expected to take a very long time. On the other hand, if the CTL response is short lived in the absence of antigen, virus replicates at higher levels and is only opposed by a narrow CTL response, characterized by an immunodominant CTL clone. In this case, antigenic escape is expected to evolve in a short period of time, resulting in progressive loss of virus control. We discuss our findings in relation to data from HIV-1-infected patients.

Correlates of cytotoxic T-lymphocyte-mediated virus control: implications for immunosuppressive infections and their treatment

A very important question in immunology is to determine which factors decide whether an immune response can efficiently clear or control a viral infection, and under what circumstances we observe persistent viral replication and pathology. This paper summarizes how mathematical models help us gain new insights into these questions, and explores the relationship between antiviral therapy and long-term immunological control in human immunodeficiency virus (HIV) infection. We find that cytotoxic T lymphocyte (CTL) memory, defined as antigen-independent persistence of CTL precursors, is necessary for the CTL response to clear an infection. The presence of such a memory response is associated with the coexistence of many CTL clones directed against multiple epitopes. If CTL memory is inefficient, then persistent replication can be established. This outcome is associated with a narrow CTL response directed against only one or a few viral epitopes. If the virus replicates persistently, occurrence of pathology depends on the level of virus load at equilibrium, and this can be determined by the overall efficacy of the CTL response. Mathematical models suggest that controlled replication is reflected by a positive correlation between CTLs and virus load. On the other hand, uncontrolled viral replication results in higher loads and the absence of a correlation between CTLs and virus load. A negative correlation between CTLs and virus load indicates that the virus actively impairs immunity, as observed with HIV. Mathematical models and experimental data suggest that HIV persistence and pathology are caused by the absence of sufficient CTL memory. We show how mathematical models can help us devise therapy regimens that can restore CTL memory in HIV patients and result in long-term immunological control of the virus in the absence of life-long treatment.

Transient antiretroviral treatment during acute simian immunodeficiency virus infection facilitates long-term control of the virus

Experimental evidence and mathematical models indicate that CD4+ T-cell help is required to generate memory cytotoxicT-lymphocyte precursors (CTLp) that are capable of persisting without ongoing antigenic stimulation, and that such responses are necessary to clear an infection or to control it in the long term. Here we analyse mathematical models of simian immunodeficiency virus (SIV) replication in macaques, assuming that SIV impairs specific CD4+ T-cell responses. According to the models, fast viral replication during the initial stages of primary infection can result in failure to generate sufficient long-lived memory CTLp required to control the infection in the long term. Modelling of drug therapy during the acute phase of the infection indicates that transient treatment can minimize the amount of virus-induced immune impairment, allowing a more effective initial immune sensitization. The result is the development of high levels of memory CTLp that are capable of controlling SIV replication in the long term, in the absence of continuous treament. In the model, the success of treatment depends crucially on the timing and duration of antiretroviral therapy. Data on SIV-infected macaques receiving transient drug therapy during acute infection support these theoretical predictions. The data and modelling suggest that among subjects controlling SIV replication most efficiently after treatment, there is a positive correlation between cellular immune responses and virus load in the post-acute stage of infection. Among subjects showing less-efficient virus control, the correlation is negative. We discuss our findings in relation to previously published data on HIV infection.

Nash equilibria for an evolutionary language game

We study an evolutionary language game that describes how signals become associated with meaning. In our context, a language, L, is described by two matrices: the P matrix contains the probabilities that for a speaker certain objects are associated with certain signals, while the Q matrix contains the probabilities that for a listener certain signals are associated with certain objects. We define the payoff in our evolutionary language game as the total amount of information exchanged between two individuals. We give a formal classification of all languages, L(P, Q), describing the conditions for Nash equilibria and evolutionarily stable strategies (ESS). We describe an algorithm for generating all languages that are Nash equilibria. Finally, we show that starting from any random language, there exists an evolutionary trajectory using selection and neutral drift that ends up with a strategy that is a strict Nash equilibrium (or very close to a strict Nash equilibrium).

Language evolution and information theory

This paper places models of language evolution within the framework of information theory. We study how signals become associated with meaning. If there is a probability of mistaking signals for each other, then evolution leads to an error limit: increasing the number of signals does not increase the fitness of a language beyond a certain limit. This error limit can be overcome by word formation: a linear increase of the word length leads to an exponential increase of the maximum fitness. We develop a general model of word formation and demonstrate the connection between the error limit and Shannon's noisy coding theorem.

HIV-1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing?

The biphasic decay of blood viraemia in patients being treated for human immunodeficiency virus type 1 (HIV-1) infection has been explained as the decay of two distinct populations of cells: the rapid death of productively infected cells followed by the much slower elimination of a second population the identity of which remains unknown. Here we advance an alternative explanation based on the immune response against a single population of infected cells. We show that the biphasic decay can be explained simply, without invoking multiple compartments: viral load falls quickly while cytotoxic T lymphocytes (CTL) are still abundant, and more slowly as CTL disappear. We propose a method to test this idea, and develop a framework that is readily applicable to treatment of other infections.

Competitive coexistence in antiviral immunity

Adaptive immunity to viruses in vertebrates is mediated by two distinct but complementary branches of the immune system: the cellular response, which eliminates infected cells, and the humoral response, which eliminates infectious virus. This leads to an interesting contest, since the two responses compete, albeit indirectly, for proliferative stimuli. How can a host mount a coordinated antiviral campaign? Here we show that competition may lead to a state of "competitive coexistence" in which, counterintuitively, each branch complements the other, with clinical benefit to the host. The principle is similar to free-market economics, in which firms compete, but the consumer benefits. Experimental evidence suggests this is a useful paradigm in antiviral immunity.

The basic reproductive ratio of a word, the maximum size of a lexicon

Language is about words and rules. While there is some discussion to what extent rules are learned or innate, it is clear that words have to be learned. Here I construct a mathematical framework for the population dynamics of language evolution with particular emphasis on how words are propagated over generations. I define the basic reproductive ratio of word, R, and show that R > 1 is required for words to be maintained in the lexicon of a language. Assuming that the frequency distribution of words follow Zipf's law, an upper limit is obtained for the number of words in a language that relies exclusively on oral transmission.

Direct quantitation of rapid elimination of viral antigen-positive lymphocytes by antiviral CD8(+) T cells in vivo

Lysis of infected cells by CD8(+) T cells is an important mechanism for the control of virus infections, but remains difficult to quantify in vivo. Here, we study the elimination kinetics of viral antigen-positive lymphocytes by antiviral CD8(+) T cells using flow cytometry and mathematical analysis. In mice acutely infected with lymphocytic choriomeningitis virus, more than 99.99 % of target cells were eliminated each day, corresponding to a half-life of 1.4 h. Even in mice exposed to virus 300 days previously, and with no ex vivo killing activity, 84 % of the target cells were eliminated per day. Unexpectedly, the elimination kinetics of antigen-positive lymphocytes was not significantly impaired in mice deficient in either perforin-, CD95 ligand- or TNF-mediated cytotoxicity. For viruses with a particular tropism for lymphocytes, such as Epstein-Barr virus or HIV, our results illustrate how effectively CD8(+) T cell-mediated elimination of target cells can potentially contribute to virus control and immunosuppression.

Adherence and drug resistance: predictions for therapy outcome

We combine standard pharmacokinetics with an established model of viral replication to predict the outcome of therapy as a function of adherence to the drug regimen. We consider two types of treatment failure: failure to eliminate the wild-type virus, and the emergence of drug-resistant virus. Specifically, we determine the conditions under which resistance dominates as a result of imperfect adherence. We derive this result for both single- and triple-drug therapies, with attention to conditions which favour the emergence of viral strains that are resistant to one or more drugs in a cocktail. Our analysis provides quantitative estimates of the degree of adherence necessary to prevent resistance. We derive results specific to the treatment of human immunodeficiency virus infection, but emphasize that our method is applicable to a range of viral or other infections treated by chemotherapy.

The role of antigen-independent persistence of memory cytotoxic T lymphocytes

We use mathematical models to analyze the role of a memory cytotoxic T lymphocyte (CTL) response in viral infections. The model predicts that antigen-independent persistence of an elevated number of precursor CTL (CTLp) does not protect the host from clinical symptoms upon re-infection. Instead, we find that antigen-independent long-term persistence of CTLp is required to clear virus infections. This mechanism also applies to infection in hosts that have never experienced the pathogen before. Requirement of antigen for the long-term maintenance of CTLp results in failure to clear the infection, even in hosts characterized by a high CTL responsiveness. We compare the CTL model to a B cell model. In keeping with experimentally established findings, B cells are efficient in protecting against re-infection, but are unlikely to clear viral infections unless the virus is cytopathic. We conclude that the role of 'memory CTLp' is different from the role of memory B cells in viral infections: antigen-independent long-term persistence of CTLp is a pre-requisite to ensure clearance of infection.

The evolution of syntactic communication

Animal communication is typically non-syntactic, which means that signals refer to whole situations. Human language is syntactic, and signals consist of discrete components that have their own meanings. Syntax is a prerequisite for taking advantage of combinatorics, that is, "making infinite use of finite means. The vast expressive power of human language would be impossible without syntax, and the transition from non-syntactic to syntactic communication was an essential step in the evolution of human language. We aim to understand the evolutionary dynamics of this transition and to analyse how natural selection can guide it. Here we present a model for the population dynamics of language evolution, define the basic reproductive ratio of words and calculate the maximum size of a lexicon. Syntax allows larger repertoires and the possibility to formulate messages that have not been learned beforehand. Nevertheless, according to our model natural selection can only favour the emergence of syntax if the number of required signals exceeds a threshold value. This result might explain why only humans evolved syntactic communication and hence complex language.