pwc-archive/papers-with-abstracts huggingface dataset:
Autocratic strategies for iterated games with arbitrary action spaces
Date: 2016-04-11 00:00:00

The recent discovery of zero-determinant strategies for the iterated
Prisoner's Dilemma sparked a surge of interest in the surprising fact that a
player can exert unilateral control over iterated interactions. These
remarkable strategies, however, are known to exist only in games in which
players choose between two alternative actions such as "cooperate" and
"defect." Here we introduce a broader class of autocratic strategies by
extending zero-determinant strategies to iterated games with more general
action spaces. We use the continuous Donation Game as an example, which
represents an instance of the Prisoner's Dilemma that intuitively extends to a
continuous range of cooperation levels. Surprisingly, despite the fact that the
opponent has infinitely many donation levels from which to choose, a player can
devise an autocratic strategy to enforce a linear relationship between his or
her payoff and that of the opponent even when restricting his or her actions to
merely two discrete levels of cooperation. In particular, a player can use such
a strategy to extort an unfair share of the payoffs from the opponent.
Therefore, although the action space of the continuous Donation Game dwarfs
that of the classical Prisoner's Dilemma, players can still devise relatively
simple autocratic and, in particular, extortionate strategies.
Optimal Portfolio Liquidation and Dynamic Mean-variance Criterion
Date: 2015-10-30 00:00:00

In this paper, we consider the optimal portfolio liquidation problem under
the dynamic mean-variance criterion and derive time-consistent solutions in
three important models. We give adapted optimal strategies under a reconsidered
mean-variance subject at any point in time. We get explicit trading strategies
in the basic model and when random pricing signals are incorporated. When we
consider stochastic liquidity and volatility, we construct a generalized HJB
equation under general assumptions for the parameters. We obtain an explicit
solution in stochastic volatility model with a given structure supported by
empirical studies.
Paired spiking robustly shapes spontaneous activity in neural networks in vitro
Date: 2015-10-30 00:00:00
Tasks: Cultural Vocal Bursts Intensity Prediction, Functional Connectivity

In vivo, neurons establish functional connections and preserve information
along their synaptic pathways from one information processing stage to the next
in a very efficient manner. Paired spiking (PS) enhancement plays a key role by
acting as a temporal filter that deletes less informative spikes. We analyzed
the spontaneous neural activity evolution in a hippocampal and a cortical
network over several weeks exploring whether the same PS coding mechanism
appears in neuronal cultures as well. We show that self-organized neural in
vitro networks not only develop characteristic bursting activity, but feature
robust in vivo-like PS activity. PS activity formed spatiotemporal patterns
that started at early days in vitro (DIVs) and lasted until the end of the
recording sessions. Initially random-like and sparse PS patterns became robust
after three weeks in vitro (WIVs). They were characterized by a high number of
occurrences and short inter-paired spike intervals (IPSIs). Spatially, the
degree of complexity increased by recruiting new neighboring sites in PS as a
culture matured. Moreover, PS activity participated in establishing functional
connectivity between different sites within the developing network. Employing
transfer entropy (TE) as an information transfer measure, we show that PS
activity is robustly involved in establishing effective connectivities. Spiking
activity at both individual sites and network level robustly followed each PS
within a short time interval. PS may thus be considered a spiking predictor.
These findings suggest that PS activity is preserved in spontaneously active in
vitro networks as part of a robust coding mechanism as encountered in vivo. We
suggest that, presumably in lack of any external sensory stimuli, PS may act as
an internal surrogate stimulus to drive neural activity at different
developmental stages.
A characterization of minimum spanning tree-like metric spaces
Date: 2015-10-30 00:00:00

Recent years have witnessed a surge of biological interest in the minimum
spanning tree (MST) problem for its relevance to automatic model construction
using the distances between data points. Despite the increasing use of MST
algorithms for this purpose, the goodness-of-fit of an MST to the data is often
elusive because no quantitative criteria have been developed to measure it.
Motivated by this, we provide a necessary and sufficient condition to ensure
that a metric space on n points can be represented by a fully labeled tree on n
vertices, and thereby determine when an MST preserves all pairwise distances
between points in a finite metric space.
Individual-based approach to epidemic processes on arbitrary dynamic contact networks
Date: 2015-10-30 00:00:00

The dynamics of contact networks and epidemics of infectious diseases often
occur on comparable time scales. Ignoring one of these time scales may provide
an incomplete understanding of the population dynamics of the infection
process. We develop an individual-based approximation for the
susceptible-infected-recovered epidemic model applicable to arbitrary dynamic
networks. Our framework provides, at the individual-level, the probability flow
over time associated with the infection dynamics. This computationally
efficient framework discards the correlation between the states of different
nodes, yet provides accurate results in approximating direct numerical
simulations. It naturally captures the temporal heterogeneities and
correlations of contact sequences, fundamental ingredients regulating the
timing and size of an epidemic outbreak. Using real-life data, we show that the
static network model overestimates the reproduction number but underestimates
the infection potential of super-spreading individuals. The high accuracy of
our approximation further allows us to detect the index individual of an
epidemic outbreak.
Pathwise no-arbitrage in a class of Delta hedging strategies
Date: 2016-06-15 00:00:00

We consider a strictly pathwise setting for Delta hedging exotic options,
based on F\"ollmer's pathwise It\=o calculus. Price trajectories are
$d$-dimensional continuous functions whose pathwise quadratic variations and
covariations are determined by a given local volatility matrix. The existence
of Delta hedging strategies in this pathwise setting is established via
existence results for recursive schemes of parabolic Cauchy problems and via
the existence of functional Cauchy problems on path space. Our main results
establish the nonexistence of pathwise arbitrage opportunities in classes of
strategies containing these Delta hedging strategies and under relatively mild
conditions on the local volatility matrix.
Formalized Quantum Stochastic Processes and Hidden Quantum Models with Applications to Neuron Ion Channel Kinetics
Authors: Alan Paris, George Atia, Azadeh Vosoughi, Stephen Berman
Date: 2015-10-31 00:00:00

A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating $S(f) \sim 1/f^\alpha$, thus offering a biophysical explanation for the ubiquitous $1/f$-type in neurological signals.
Spatial measures of genetic heterogeneity during carcinogenesis
Date: 2015-10-31 00:00:00
Tasks: Diversity

In this work we explore the temporal dynamics of spatial heterogeneity during
the process of tumorigenesis from healthy tissue. We utilize a spatial
stochastic process model of mutation accumulation and clonal expansion in a
structured tissue to describe this process. Under a two-step tumorigenesis
model, we first derive estimates of a non-spatial measure of diversity:
Simpson's Index, which is the probability that two individuals sampled at
random from the population are identical, in the premalignant population. We
next analyze two new measures of spatial population heterogeneity. In
particular we study the typical length scale of genetic heterogeneity during
the carcinogenesis process and estimate the extent of a surrounding
premalignant clone given a clinical observation of a premalignant point biopsy.
This evolutionary framework contributes to a growing literature focused on
developing a better understanding of the spatial population dynamics of cancer
initiation and progression. Although initially motivated by understanding
questions in cancer, these results can be applied more generally to help
understand the dynamics of heterogeneity and diversity in a variety of
spatially structured, evolving populations.
A New Class of Problems in the Calculus of Variations
Date: 2015-10-31 00:00:00

This paper investigates an infinite-horizon problems in the one-dimensional
calculus of variations, arising from the Ramsey model of endogeneous economic
growth. Following Chichilnisky, we introduce an additional term, which models
concern for the well-being of future generations. We show that there are no
optimal solutions, but that there are equilibrium strateges, i.e. Nash
equilibria of the leader-follower game between successive generations. To solve
the problem, we approximate the Chichilnisky criterion by a biexponential
criterion, we characterize its equilibria by a pair of coupled differential
equations of HJB type, and we go to the limit. We find all the equilibrium
strategies for the Chichilnisky criterion. The mathematical analysis is
difficult because one has to solve an implicit differential equation in the
sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak. It is
shown that optimal solutions a class of problems raising from time
inconsistency problems in the framework of the neoclassical one-sector model of
economic growth, and contains new results in environment economics. Without
exogenous commitment mechanism, a notion of the equilibrium strategies instead
of the optimal strategies is introduced. We characterized the equilibrium
strategies by an integro-differential equation system. For two special
criteria, the bi-exponential criteria and the Chichilnisky criteria, we
established the existence of the equilibrium strategies.
repgenHMM: a dynamic programming tool to infer the rules of immune receptor generation from sequence data
Date: 2015-10-31 00:00:00
Tasks: Diversity

The diversity of the immune repertoire is initially generated by random
rearrangements of the receptor gene during early T and B cell development.
Rearrangement scenarios are composed of random events -- choices of gene
templates, base pair deletions and insertions -- described by probability
distributions. Not all scenarios are equally likely, and the same receptor
sequence may be obtained in several different ways. Quantifying the
distribution of these rearrangements is an essential baseline for studying the
immune system diversity. Inferring the properties of the distributions from
receptor sequences is a computationally hard problem, requiring enumerating
every possible scenario for every sampled receptor sequence. We present a
Hidden Markov model, which accounts for all plausible scenarios that can
generate the receptor sequences. We developed and implemented a method based on
the Baum-Welch algorithm that can efficiently infer the parameters for the
different events of the rearrangement process. We tested our software tool on
sequence data for both the alpha and beta chains of the T cell receptor. To
test the validity of our algorithm, we also generated synthetic sequences
produced by a known model, and confirmed that its parameters could be
accurately inferred back from the sequences. The inferred model can be used to
generate synthetic sequences, to calculate the probability of generation of any
receptor sequence, as well as the theoretical diversity of the repertoire. We
estimate this diversity to be $\approx 10^{23}$ for human T cells. The model
gives a baseline to investigate the selection and dynamics of immune
repertoires.
Common basis for cellular motility
Date: 2015-10-31 00:00:00

Motility is characteristic of life, but a common basis for movement has
remained to be identified. Diverse systems in motion shift between two states
depending on interactions that turnover at the rate of an applied cycle of
force. Although one phase of the force cycle terminates the decay of the most
recent state, continuation of the cycle of force regenerates the original decay
process in a recursive cycle. By completing a cycle, kinetic energy is
transformed into probability of sustaining the most recent state and the system
gains a frame of reference for discrete transitions having static rather than
time-dependent probability. The probability of completing a recursive cycle is
computed with a Markov chain comprised of two equilibrium states and a kinetic
intermediate. Given rate constants for the reactions, a random walk reproduces
bias and recurrence times of walking motor molecules and bacterial flagellar
switching with unrivaled fidelity.
Chaos of Protein Folding
Date: 2015-10-31 00:00:00
Tasks: Protein Folding

As protein folding is a NP-complete problem, artificial intelligence tools
like neural networks and genetic algorithms are used to attempt to predict the
3D shape of an amino acids sequence. Underlying these attempts, it is supposed
that this folding process is predictable. However, to the best of our
knowledge, this important assumption has been neither proven, nor studied. In
this paper the topological dynamic of protein folding is evaluated. It is
mathematically established that protein folding in 2D hydrophobic-hydrophilic
(HP) square lattice model is chaotic as defined by Devaney. Consequences for
both structure prediction and biology are then outlined.
Conditional Value-at-Risk: Theory and Applications
Date: 2015-10-31 00:00:00

This thesis presents the Conditional Value-at-Risk concept and combines an
analysis that covers its application as a risk measure and as a vector norm.
For both areas of application the theory is revised in detail and examples are
given to show how to apply the concept in practice.
  In the first part, CVaR as a risk measure is introduced and the analysis
covers the mathematical definition of CVaR and different methods to calculate
it. Then, CVaR optimization is analysed in the context of portfolio selection
and how to apply CVaR optimization for hedging a portfolio consisting of
options. The original contributions in this part are an alternative proof of
Acerbi's Integral Formula in the continuous case and an explicit programme
formulation for portfolio hedging.
  The second part first analyses the Scaled and Non-Scaled CVaR norm as new
family of norms in $\mathbb{R}^n$ and compares this new norm family to the more
widely known $L_p$ norms. Then, model (or signal) recovery problems are
discussed and it is described how appropriate norms can be used to recover a
signal with less observations than the dimension of the signal. The last
chapter of this dissertation then shows how the Non-Scaled CVaR norm can be
used in this model recovery context. The original contributions in this part
are an alternative proof of the equivalence of two different characterizations
of the Scaled CVaR norm, a new proposition that the Scaled CVaR norm is
piecewise convex, and the entire \autoref{chapter:Recovery_using_CVaR}. Since
the CVaR norm is a rather novel concept, its applications in a model recovery
context have not been researched yet. Therefore, the final chapter of this
thesis might lay the basis for further research in this area.
Neural ring homomorphisms and maps between neural codes
Date: 2019-02-13 00:00:00

Neural codes are binary codes that are used for information processing and
representation in the brain. In previous work, we have shown how an algebraic
structure, called the {\it neural ring}, can be used to efficiently encode
geometric and combinatorial properties of a neural code [1]. In this work, we
consider maps between neural codes and the associated homomorphisms of their
neural rings. In order to ensure that these maps are meaningful and preserve
relevant structure, we find that we need additional constraints on the ring
homomorphisms. This motivates us to define {\it neural ring homomorphisms}. Our
main results characterize all code maps corresponding to neural ring
homomorphisms as compositions of 5 elementary code maps. As an application, we
find that neural ring homomorphisms behave nicely with respect to convexity. In
particular, if $\mathcal{C}$ and $\mathcal{D}$ are convex codes, the existence
of a surjective code map $\mathcal{C}\rightarrow \mathcal{D}$ with a
corresponding neural ring homomorphism implies that the minimal embedding
dimensions satisfy $d(\mathcal{D}) \leq d(\mathcal{C})$.
Nonequilibrium dissipation in living oocytes
Date: 2016-12-22 00:00:00

Living organisms are inherently out-of-equilibrium systems. We employ new
developments in stochastic energetics and rely on a minimal microscopic model
to predict the amount of mechanical energy dissipated by such dynamics. Our
model includes complex rheological effects and nonequilibrium stochastic
forces. By performing active microrheology and tracking micron-sized vesicles
in the cytoplasm of living oocytes, we provide unprecedented measurements of
the spectrum of dissipated energy. We show that our model is fully consistent
with the experimental data, and we use it to offer predictions for the
injection and dissipation energy scales involved in active fluctuations.
Network Models in Epidemiology: Considering Discrete and Continuous Dynamics
Date: 2015-10-19 00:00:00
Tasks: Articles, Epidemiology

Discrete and Continuous Dynamics is the first in a series of articles on
Network Models for Epidemiology. This project began in the Fall quarter of 2014
in my continuous modeling course. Since then, it has taken off and turned into
a series of articles, which I hope to compile into a single report. The purpose
of the report is to explore mathematical epidemiology. In this article, we
discuss the historical approach to disease modeling with compartmental models.
We discuss the issues and benefits of using network models. We build a discrete
dynamical system to describe infection and recovery of individuals in the
population. Lastly, we detail the computational scheme for iterating this
model.
Trajectory based models. Evaluation of minmax pricing bounds
Date: 2016-12-21 00:00:00

The paper studies sub and super-replication price bounds for contingent
claims defined on general trajectory based market models. No prior
probabilistic or topological assumptions are placed on the trajectory space,
trading is assumed to take place at a finite number of occasions but not
bounded in number nor necessarily equally spaced in time. For a given option,
there exists an interval bounding the set of possible fair prices; such
interval exists under more general conditions than the usual no-arbitrage
requirement. The paper develops a backward recursive method to evaluate the
option bounds; the global minmax optimization, defining the price interval, is
reduced to a local minmax optimization via dynamic programming. Trajectory sets
are introduced for which existing non-probabilistic markets models are nested
as a particular case. Several examples are presented, the effect of the
presence of arbitrage on the price bounds is illustrated.
The wisdom of networks: A general adaptation and learning mechanism of complex systems: The network core triggers fast responses to known stimuli; innovations require the slow network periphery and are encoded by core-remodeling
Date: 2018-02-23 00:00:00
Tasks: Decision Making, Learning Theory

I hypothesize that re-occurring prior experience of complex systems mobilizes
a fast response, whose attractor is encoded by their strongly connected network
core. In contrast, responses to novel stimuli are often slow and require the
weakly connected network periphery. Upon repeated stimulus, peripheral network
nodes remodel the network core that encodes the attractor of the new response.
This "core-periphery learning" theory reviews and generalizes the heretofore
fragmented knowledge on attractor formation by neural networks,
periphery-driven innovation and a number of recent reports on the adaptation of
protein, neuronal and social networks. The coreperiphery learning theory may
increase our understanding of signaling, memory formation, information encoding
and decision-making processes. Moreover, the power of network periphery-related
'wisdom of crowds' inventing creative, novel responses indicates that
deliberative democracy is a slow yet efficient learning strategy developed as
the success of a billion-year evolution.
Universality classes of foraging with resource renewal
Date: 2016-01-14 00:00:00

We determine the impact of resource renewal on the lifetime of a forager that
depletes its environment and starves if it wanders too long without eating. In
the framework of the minimal starving random walk model with resource renewal,
there are three universal classes of behavior as a function of the renewal
time. For sufficiently rapid renewal, foragers are immortal, while foragers
have a finite lifetime otherwise. In one dimension, there is a third regime,
for sufficiently slow renewal, in which the lifetime of the forager is
independent of the renewal time. We outline an enumeration method to determine
the mean lifetime of the forager in the mortal regime.