Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Unifying theory of hypoxia tolerance: molecular/metabolic defense and rescue mechanisms for surviving oxygen lack.

We develop a unifying theory of hypoxia tolerance based on information from two cell level models (brain cortical cells and isolated hepatocytes) from the highly anoxia tolerant aquatic turtle and from other more hypoxia sensitive systems. We propose that the response of hypoxia tolerant systems to oxygen lack occurs in two phases (defense and rescue). The first lines of defense against hypoxia include a balanced suppression of ATP-demand and ATP-supply pathways; this regulation stabilizes (adenylates) at new steady-state levels even while ATP turnover rates greatly decline. The ATP demands of ion pumping are down-regulated by generalized "channel" arrest in hepatocytes and by "spike" arrest in neurons. Hypoxic ATP demands of protein synthesis are down-regulated probably by translational arrest. In hypoxia sensitive cells this translational arrest seems irreversible, but hypoxia-tolerant systems activate "rescue" mechanisms if the period of oxygen lack is extended by preferentially regulating the expression of several proteins. In these cells, a cascade of processes underpinning hypoxia rescue and defense begins with an oxygen sensor (a heme protein) and a signal-transduction pathway, which leads to significant gene-based metabolic reprogramming-the rescue process-with maintained down-regulation of energy-demand and energy-supply pathways in metabolism throughout the hypoxic period. This recent work begins to clarify how normoxic maintenance ATP turnover rates can be drastically (10-fold) down-regulated to a new hypometabolic steady state, which is prerequisite for surviving prolonged hypoxia or anoxia. The implications of these developments are extensive in biology and medicine.

An information theory model of hydrophobic interactions.

A molecular model of poorly understood hydrophobic effects is heuristically developed using the methods of information theory. Because primitive hydrophobic effects can be tied to the probability of observing a molecular-sized cavity in the solvent, the probability distribution of the number of solvent centers in a cavity volume is modeled on the basis of the two moments available from the density and radial distribution of oxygen atoms in liquid water. The modeled distribution then yields the probability that no solvent centers are found in the cavity volume. This model is shown to account quantitatively for the central hydrophobic phenomena of cavity formation and association of inert gas solutes. The connection of information theory to statistical thermodynamics provides a basis for clarification of hydrophobic effects. The simplicity and flexibility of the approach suggest that it should permit applications to conformational equilibria of nonpolar solutes and hydrophobic residues in biopolymers.

Recruitment and replacement of hippocampal neurons in young and adult chickadees: an addition to the theory of hippocampal learning.

We used [3H]thymidine to document the birth of neurons and their recruitment into the hippocampal complex (HC) of juvenile (4.5 months old) and adult blackcapped chickadees (Parus atricapillus) living in their natural surroundings. Birds received a single dose of [3H]thymidine in August and were recaptured and killed 6 weeks later, in early October. All brains were stained with Cresyl violet, a Nissl stain. The boundaries of the HC were defined by reference to the ventricular wall, the brain surface, or differences in neuronal packing density. The HC of juveniles was as large as or larger than that of adults and packing density of HC neurons was 31% higher in juveniles than in adults. Almost all of the 3H-labeled HC neurons were found in a 350-m-wide layer of tissue adjacent to the lateral ventricle. Within this layer the fraction of 3H-labeled neurons was 50% higher in juveniles than in adults. We conclude that the HC of juvenile chickadees recruits more neurons and has more neurons than that of adults. We speculate that juveniles encounter greater environmental novelty than adults and that the greater number of HC neurons found in juveniles allows them to learn more than adults. At a more general level, we suggest that (i) long-term learning alters HC neurons irreversibly; (ii) sustained hippocampal learning requires the periodic replacement of HC neurons; (iii) memories coded by hippocampal neurons are transferred elsewhere before the neurons are replaced.

An evolutionary theory of the family.

An evolutionary framework for viewing the formation, the stability, the organizational structure, and the social dynamics of biological families is developed. This framework is based upon three conceptual pillars: ecological constraints theory, inclusive fitness theory, and reproductive skew theory. I offer a set of 15 predictions pertaining to living within family groups. The logic of each is discussed, and empirical evidence from family-living vertebrates is summarized. I argue that knowledge of four basic parameters, (i) genetic relatedness, (ii) social dominance, (iii) the benefits of group living, and (iv) the probable success of independent reproduction, can explain many aspects of family life in birds and mammals. I suggest that this evolutionary perspective will provide insights into understanding human family systems as well.

Evidence against the exon theory of genes derived from the triose-phosphate isomerase gene.

The exon theory of genes proposes that the introns of protein-encoding nuclear genes are remnants of the DNA spacers between ancient minigenes. The discovery of an intron at a predicted position in the triose-phosphate isomerase (EC 5.3.1.1) gene of Culex mosquitoes has been hailed as an evidential pillar of the theory. We have found that that intron is also present in Aedes mosquitoes, which are closely related to Culex, but not in the phylogenetically more distant Anopheles, nor in the fly Calliphora vicina, nor in the moth Spodoptera littoralis. The presence of this intron in Culex and Aedes is parsimoniously explained as the result of an insertion in a recent common ancestor of these two species rather than as the remnant of an ancient intron. The absence of the intron in 19 species of very diverse organisms requires at least 10 independent evolutionary losses in order to be consistent with the exon theory.

Seven newly discovered intron positions in the triose-phosphate isomerase gene: evidence for the introns-late theory.

The gene encoding the glycolytic enzyme triose-phosphate isomerase (TPI; EC 5.3.1.1) has been central to the long-standing controversy on the origin and evolutionary significance of spliceosomal introns by virtue of its pivotal support for the introns-early view, or exon theory of genes. Putative correlations between intron positions and TPI protein structure have led to the conjecture that the gene was assembled by exon shuffling, and five TPI intron positions are old by the criterion of being conserved between animals and plants. We have sequenced TPI genes from three diverse eukaryotes--the basidiomycete Coprinus cinereus, the nematode Caenorhabditis elegans, and the insect Heliothis virescens--and have found introns at seven novel positions that disrupt previously recognized gene/protein structure correlations. The set of 21 TPI introns now known is consistent with a random model of intron insertion. Twelve of the 21 TPI introns appear to be of recent origin since each is present in but a single examined species. These results, together with their implication that as more TPI genes are sequenced more intron positions will be found, render TPI untenable as a paradigm for the introns-early theory and, instead, support the introns-late view that spliceosomal introns have been inserted into preexisting genes during eukaryotic evolution.

Theory of orientation tuning in visual cortex.

The role of intrinsic cortical connections in processing sensory input and in generating behavioral output is poorly understood. We have examined this issue in the context of the tuning of neuronal responses in cortex to the orientation of a visual stimulus. We analytically study a simple network model that incorporates both orientation-selective input from the lateral geniculate nucleus and orientation-specific cortical interactions. Depending on the model parameters, the network exhibits orientation selectivity that originates from within the cortex, by a symmetry-breaking mechanism. In this case, the width of the orientation tuning can be sharp even if the lateral geniculate nucleus inputs are only weakly anisotropic. By using our model, several experimental consequences of this cortical mechanism of orientation tuning are derived. The tuning width is relatively independent of the contrast and angular anisotropy of the visual stimulus. The transient population response to changing of the stimulus orientation exhibits a slow "virtual rotation." Neuronal cross-correlations exhibit long time tails, the sign of which depends on the preferred orientations of the cells and the stimulus orientation.