pwc-archive/papers-with-abstracts huggingface dataset:
Pricing of high-dimensional options
Date: 2015-10-25 00:00:00
Tasks: Vocal Bursts Intensity Prediction

Pricing of high-dimensional options is one of the most important problems in
Mathematical Finance. The objective of this manuscript is to present an
original self-contained treatment of the multidimensional pricing. During the
past decades the Black-Scholes this model, which essentially is based on the
log-normal assumption, has been increasingly criticised. In particular, it was
noticed by Mandelbrot that empirical log-returns distributions are more
concentrated around the origin and have considerably heavier tails. This
suggests to adjust the Black-Scholes model by the introduction of the Levy
processes instead of Brownian ones. This approach has been extensively studied
in a univariate setup since the nineties. In the multivariate settings the
theory is not so advanced. We present a general method of high-dimensional
option pricing based on a wide range of jump-diffusion models. Namely, we
construct approximation formulas for the price of spread options. It is
important to get an efficient approximation for the respective density
function, since the reward function has usually a simple structure. Instead of
a commonly used tabulation approach, we use the respective m-widths to compare
a wide range of numerical methods. We give an algorithm of almost optimal, in
the sense of the respective m-widths, reconstruction of density functions. To
demonstrate the power of our approach we consider in details a concrete class
of Levy driven processes and present the respective rates of convergence of
approximation formulas. The interrelationship between the theory and tools
reflects the richness and deep connections in Financial Mathematics, Stochastic
Processes, Theory of Martingales, Functional Analysis, Topology and Harmonic
Analysis.
Dynamical Complexity in the C.elegans Neural Network
Date: 2015-10-25 00:00:00

We model the neuronal circuit of the C.elegans soil worm in terms of
Hindmarsh-Rose systems of ordinary differential equations, dividing its circuit
into six communities pointed out by the walktrap and Louvain methods. Using the
numerical solution of these equations, we analyze important measures of
dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and
the $\Phi_{\mbox{AR}}$ auto-regressive integrated information theory measure,
which has been suggested to reflect different levels of consciousness. We show
that $\Phi_{\mbox{AR}}$ provides a useful measure of the information contained
in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans
brain dynamic network generates more information than the sum of its
constituent parts, and that attains higher levels of integrated information for
couplings for which either all its communities are highly synchronized, or
there is a mixed state of highly synchronized and desynchronized communities.
Both situations are characterized by relatively low chaotic behavior.
Uncovering the evolution of non-stationary stochastic variables: the example of asset volume-price fluctuations
Date: 2015-10-25 00:00:00
Tasks: Geophysics, Time Series, Time Series Analysis

We present a framework for describing the evolution of stochastic observables
having a non-stationary distribution of values. The framework is applied to
empirical volume-prices from assets traded at the New York stock exchange.
Using Kullback-Leibler divergence we evaluate the best model out from four
biparametric models standardly used in the context of financial data analysis.
In our present data sets we conclude that the inverse $\Gamma$-distribution is
a good model, particularly for the distribution tail of the largest
volume-price fluctuations. Extracting the time-series of the corresponding
parameter values we show that they evolve in time as stochastic variables
themselves. For the particular case of the parameter controlling the
volume-price distribution tail we are able to extract an Ornstein-Uhlenbeck
equation which describes the fluctuations of the largest volume-prices observed
in the data. Finally, we discuss how to bridge from the stochastic evolution of
the distribution parameters to the stochastic evolution of the (non-stationary)
observable and put our conclusions into perspective for other applications in
geophysics and biology.
Wavelet-Based Compression and Peak Detection Method for the Experimentally Estimation of Microtubules Dynamic Instability Parameters Identified in Three States
Date: 2015-10-25 00:00:00
Tasks: parameter estimation

Recent studies has revealed that Microtubules (MTs) exhibit three transition
states of growth, shrinkage and pause. In this paper, we first introduce a
three states random evolution model as a framework for studying MTs dynamics in
three transition states of growth, pause and shrinkage. Then, we introduce a
non-traditional stack run encoding scheme with 5 symbols for detecting
transition states as well as to encode MT experimental data. The peak detection
is carried out in the wavelet domain to effectively detect these three
transition states. One of the added advantages of including peak information
while encoding being that it enables to detect the peaks efficiently and
encodes them simultaneously in the wavelet domain without having the need to do
further processing after the decoding stage. Experimental results show that
using this form of non-traditional stack run encoding has better compression
and reconstruction performance as opposed to traditional stack run encoding and
run length encoding schemes. Parameters for MTs modeled in the three states are
estimated and is shown to closely approximate original MT data for lower
compression rates. As the compression rate increases, we may end up throwing
away details that are required to detect transition states of MTs. Thus,
choosing the right compression rate is a trade-off between admissible level of
error in signal reconstruction, its parameter estimation and considerable rate
of compression of MT data.
Predator interference effects on biological control: The "paradox" of the generalist predator revisited
Date: 2015-10-25 00:00:00

An interesting conundrum in biological control questions the efficiency of
generalist predators as biological control agents. Theory suggests, generalist
predators are poor agents for biological control, primarily due to mutual
interference. However field evidence shows they are actually quite effective in
regulating pest densities. In this work we provide a plausible answer to this
paradox. We analyze a three species model, where a generalist top predator is
introduced into an ecosystem as a biological control, to check the population
of a middle predator, that in turn is depredating on a prey species. We show
that the inclusion of predator interference alone, can cause the solution of
the top predator equation to blow-up in finite time, while there is global
existence in the no interference case. This result shows that interference
could actually cause a population explosion of the top predator, enabling it to
control the target species, thus corroborating recent field evidence. Our
results might also partially explain the population explosion of certain
species, introduced originally for biological control purposes, such as the
cane toad (\emph{Bufo marinus}) in Australia, which now functions as a
generalist top predator. We also show both Turing instability and
spatio-temporal chaos in the model. Lastly we investigate time delay effects.
Verifying the HALE measures of the Global Burden of Disease Study: Quantitative Methods Proposed
Date: 2015-10-26 00:00:00

To verify the Global Burden of Disease Study and the provided healthy life
expectancy (HALE) estimates from the World Health Organization (WHO) we propose
a very simple model based on the mortality {\mu}x of a population provided in a
classical life table and a mortality diagram. We use the abridged life tables
provided by WHO. Our estimates are compared with the HALE estimates for the
World territories and the WHO countries. Even more we have developed the
related simple program in Excel which provides immediately the Life Expectancy,
the Loss of Healthy Life Years and the Healthy Life Expectancy estimate. We
also apply the health state function theory to have more estimates and
comparisons. The results suggest improved WHO estimates in recent years for the
majority of the cases. Keywords: Health state function, Healthy life
expectancy, Mortality Diagram, Loss of healthy years, LHLY, HALE, DALE, World
Health Organization, WHO, Global burden of Disease, Health status.
Assessing the Efficiency of \textit{Cordon Sanitaire} as a Control Strategy of Ebola
Date: 2015-10-26 00:00:00

We formulate a two-patch mathematical model for Ebola Virus Disease dynamics
in order to evaluate the effectiveness of \textit{cordons sanitaires},
mandatory movement restrictions between communities while exploring their role
on disease dynamics and final epidemic size. Simulations show that severe
restrictions in movement between high and low risk areas of closely linked
communities may have a deleterious impact on the overall levels of infection in
the total population.
Stochastic density effects on adult fish survival and implications for population fluctuations
Date: 2016-01-22 00:00:00
Tasks: Time Series, Time Series Analysis

The degree to which population fluctuations arise from variable adult
survival relative to variable recruitment has been debated widely for marine
organisms. Disentangling these effects remains challenging because data
generally are not sufficient to evaluate if and how adult survival rates are
regulated by stochasticity and/or population density. Using unique time-series
for a largely unexploited reef fish, we found both population density and
stochastic food supply impacted adult survival. The estimated effect of
variable survival on adult abundance (both mean and variability) rivaled that
of variable recruitment. Moreover, we show density dependent adult survival can
dampen impacts of stochastic recruitment. Thus, food variability may alter
population fluctuations by simultaneously regulating recruitment and
compensatory adult survival. These results provide an additional mechanism for
why intensified density independent mortality (via harvest or other means)
amplifies population fluctuations and emphasizes need for research evaluating
the causes and consequences of variability in adult survival.
Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains
Date: 2015-10-26 00:00:00

Coherent neural spiking and local field potentials are believed to be
signatures of the binding and transfer of information in the brain. Coherent
activity has now been measured experimentally in many regions of mammalian
cortex. Synfire chains are one of the main theoretical constructs that have
been appealed to to describe coherent spiking phenomena. However, for some
time, it has been known that synchronous activity in feedforward networks
asymptotically either approaches an attractor with fixed waveform and
amplitude, or fails to propagate. This has limited their ability to explain
graded neuronal responses. Recently, we have shown that pulse-gated synfire
chains are capable of propagating graded information coded in mean population
current or firing rate amplitudes. In particular, we showed that it is possible
to use one synfire chain to provide gating pulses and a second, pulse-gated
synfire chain to propagate graded information. We called these circuits
synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded
information can rapidly cascade through a neural circuit, and show a
correspondence between this type of transfer and a mean-field model in which
gating pulses overlap in time. We show that SGSCs are robust in the presence of
variability in population size, pulse timing and synaptic strength. Finally, we
demonstrate the computational capabilities of SGSC-based information coding by
implementing a self-contained, spike-based, modular neural circuit that is
triggered by, then reads in streaming input, processes the input, then makes a
decision based on the processed information and shuts itself down.
An empirical analysis of the relationships between crude oil, gold and stock markets
Date: 2016-05-24 00:00:00

This paper analyzes the direction of the causality between crude oil, gold
and stock markets for the largest economy in the world with respect to such
markets, the US. To do so, we apply non-linear Granger causality tests. We find
a nonlinear causal relationship among the three markets considered, with the
causality going in all directions, when the full sample and different
subsamples are considered. However, we find a unidirectional nonlinear causal
relationship between the crude oil and gold market (with the causality only
going from oil price changes to gold price changes) when the subsample runs
from the first date of any year between the mid-1990s and 2001 to last
available data (February 5, 2015). The latter result may explain the lack of
consensus existing in the literature about the direction of the causal link
between the crude oil and gold markets.
Modern Monetary Circuit Theory, Stability of Interconnected Banking Network, and Balance Sheet Optimization for Individual Banks
Date: 2015-10-26 00:00:00

A modern version of Monetary Circuit Theory with a particular emphasis on
stochastic underpinning mechanisms is developed. It is explained how money is
created by the banking system as a whole and by individual banks. The role of
central banks as system stabilizers and liquidity providers is elucidated. It
is shown how in the process of money creation banks become naturally
interconnected. A novel Extended Structural Default Model describing the
stability of the Interconnected Banking Network is proposed. The purpose of
banks' capital and liquidity is explained. Multi-period constrained
optimization problem for banks's balance sheet is formulated and solved in a
simple case. Both theoretical and practical aspects are covered.
Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)
Date: 2015-10-26 00:00:00
Tasks: model

Gaussian network model(GNM) and anisotropic network model(ANM) are some of
the most popular methods for the study of protein flexibility and related
functions. In this work, we propose generalized GNM(gGNM) and ANM methods and
show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter,
which is a special case of a wide class of correlation functions underpinning
the linear scaling flexibility-rigidity index(FRI) method. Based on the
mathematical structure of correlation functions, we propose a unified framework
to construct generalized Kirchhoff matrices whose matrix inverse leads to
gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI
method.With this connection,we further introduce two multiscale elastic network
models, namely, multiscale GNM(mGNM) and multiscale ANM(mANM), which are able
to incorporate different scales into the generalized Kirchkoff matrices or
generalized Hessian matrices.We validate our new multiscale methods with
extensive numerical experiments. We illustrate that gGNMs outperform the
original GNM method in the B-factor prediction of a set of 364 proteins.We
demonstrate that for a given correlation function, FRI and gGNM methods provide
essentially identical B-factor predictions when the scale value in the
correlation function is sufficiently large.More importantly,we reveal intrinsic
multiscale behavior in protein structures. The proposed mGNM and mANM are able
to capture this multiscale behavior and thus give rise to a significant
improvement of more than 11% in B-factor predictions over the original GNM and
ANM methods. We further demonstrate benefit of our mGNM in the B-factor
predictions on many proteins that fail the original GNM method. We show that
the present mGNM can also be used to analyze protein domain separations.
Finally, we showcase the ability of our mANM for the simulation of protein
collective motions.
Flexibility-Rigidity Index for Protein-Nucleic Acid Flexibility and Fluctuation Analysis
Date: 2015-10-26 00:00:00
Tasks: Specificity, Translation

Protein-nucleic acid complexes are important for many cellular processes
including the most essential function such as transcription and translation.
For many protein-nucleic acid complexes, flexibility of both macromolecules has
been shown to be critical for specificity and/or function. Flexibility-rigidity
index (FRI) has been proposed as an accurate and efficient approach for protein
flexibility analysis. In this work, we introduce FRI for the flexibility
analysis of protein-nucleic acid complexes. We demonstrate that a multiscale
strategy, which incorporates multiple kernels to capture various length scales
in biomolecular collective motions, is able to significantly improve the state
of art in the flexibility analysis of protein-nucleic acid complexes. We take
the advantage of the high accuracy and ${\cal O}(N)$ computational complexity
of our multiscale FRI method to investigate the flexibility of large ribosomal
subunits, which is difficult to analyze by alternative approaches. An
anisotropic FRI approach, which involves localized Hessian matrices, is
utilized to study the translocation dynamics in an RNA polymerase.
Stochastic robustness and relative stability of multiple pathways in biological networks
Date: 2015-10-27 00:00:00

Multiple dynamic pathways always exist in biological networks, but their
robustness against internal fluctuations and relative stability have not been
well recognized and carefully analyzed yet. Here we try to address these issues
through an illustrative example, namely the Siah-1/beta-catenin/p14/19 ARF loop
of protein p53 dynamics. Its deterministic Boolean network model predicts that
two parallel pathways with comparable magnitudes of attractive basins should
exist after the protein p53 is activated when a cell becomes harmfully
disturbed. Once the low but non-neglectable intrinsic fluctuations are
incorporated into the model, we show that a phase transition phenomenon is
emerged: in one parameter region the probability weights of the normal pathway,
reported in experimental literature, are comparable with the other pathway
which is seemingly abnormal with the unknown functions, whereas, in some other
parameter regions, the probability weight of the abnormal pathway can even
dominate and become globally attractive. The theory of exponentially perturbed
Markov chains is applied and further generalized in order to quantitatively
explain such a phase transition phenomenon, in which the nonequilibrium
"activation energy barriers" along each transiting trajectory between the
parallel pathways and the number of "optimal transition paths" play a central
part. Our theory can also determine how the transition time and the number of
optimal transition paths between the parallel pathways depend on each
interaction's strength, and help to identify those possibly more crucial
interactions in the biological network.
Overshoot during phenotypic switching of cancer cell populations
Date: 2015-10-27 00:00:00

The dynamics of tumor cell populations is hotly debated: do populations
derive hierarchically from a subpopulation of cancer stem cells (CSCs), or are
stochastic transitions that mutate differentiated cancer cells to CSCs
important? Here we argue that regulation must also be important. We sort human
melanoma cells using three distinct cancer stem cell (CSC) markers - CXCR6,
CD271 and ABCG2 - and observe that the fraction of non-CSC-marked cells first
overshoots to a higher level and then returns to the level of unsorted cells.
This clearly indicates that the CSC population is homeostatically regulated.
Combining experimental measurements with theoretical modeling and numerical
simulations, we show that the population dynamics of cancer cells is associated
with a complex miRNA network regulating the Wnt and PI3K pathways. Hence
phenotypic switching is not stochastic, but is tightly regulated by the balance
between positive and negative cells in the population. Reducing the fraction of
CSCs below a threshold triggers massive phenotypic switching, suggesting that a
therapeutic strategy based on CSC eradication is unlikely to succeed.
On the Balance of Unrooted Trees
Date: 2015-10-27 00:00:00

We solve a class of optimization problems for (phylogenetic) $X$-trees or
their shapes. These problems have recently appeared in different contexts, e.g.
in the context of the impact of tree shapes on the size of TBR neighborhoods,
but so far these problems have not been characterized and solved in a
systematic way. In this work we generalize the concept and also present several
applications. Moreover, our results give rise to a nice notion of balance for
trees. Unsurprisingly, so-called caterpillars are the most unbalanced tree
shapes, but it turns out that balanced tree shapes cannot be described so
easily as they need not even be unique.
Emergence of Cooperative Long-term Market Loyalty in Double Auction Markets
Date: 2017-08-30 00:00:00

Loyal buyer-seller relationships can arise by design, e.g. when a seller
tailors a product to a specific market niche to accomplish the best possible
returns, and buyers respond to the dedicated efforts the seller makes to meet
their needs. We ask whether it is possible, instead, for loyalty to arise
spontaneously, and in particular as a consequence of repeated interaction and
co-adaptation among the agents in a market. We devise a stylized model of
double auction markets and adaptive traders that incorporates these features.
Traders choose where to trade (which market) and how to trade (to buy or to
sell) based on their previous experience. We find that when the typical scale
of market returns (or, at fixed scale of returns, the intensity of choice)
become higher than some threshold, the preferred state of the system is
segregated: both buyers and sellers are segmented into subgroups that are
persistently loyal to one market over another. We characterize the segregated
state analytically in the limit of large markets: it is stabilized by some
agents acting cooperatively to enable trade, and provides higher rewards than
its unsegregated counterpart both for individual traders and the population as
a whole.
QPot: An R Package for Stochastic Differential Equation Quasi-Potential Analysis
Date: 2015-10-27 00:00:00

QPot is an R package for analyzing two-dimensional systems of stochastic
differential equations. It provides users with a wide range of tools to
simulate, analyze, and visualize the dynamics of these systems. One of QPot's
key features is the computation of the quasi-potential, an important tool for
studying stochastic systems. Quasi-potentials are particularly useful for
comparing the relative stabilities of equilibria in systems with alternative
stable states. This paper describes QPot's primary functions, and explains how
quasi-potentials can yield insights about the dynamics of stochastic systems.
Three worked examples guide users through the application of QPot's functions.