34,109 research outputs found
Model-counting approaches for nonlinear numerical constraints
Model counting is of central importance in quantitative rea- soning about systems. Examples include computing the probability that a system successfully accomplishes its task without errors, and measuring the number of bits leaked by a system to an adversary in Shannon entropy. Most previous work in those areas demonstrated their analysis on pro- grams with linear constraints, in which cases model counting is polynomial time. Model counting for nonlinear constraints is notoriously hard, and thus programs with nonlinear constraints are not well-studied. This paper surveys state-of-the-art techniques and tools for model counting with respect to SMT constraints, modulo the bitvector theory, since this theory is decidable, and it can express nonlinear constraints that arise from the analysis of computer programs. We integrate these techniques within the Symbolic Pathfinder platform and evaluate them on difficult nonlinear constraints generated from the analysis of cryptographic functions
A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data
The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images
Numerical simulations versus theoretical predictions for a non-Gaussian noise induced escape problem in application to full counting statistics
A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate
of a multistable system is presented. This was carried out via the estimation of an action, which is defined as
an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The
approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with
the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations
on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed
so far is discussed for an adequate characterization of the escape rate measured in experiments
Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes
We develop an arbitrage-free framework for consistent valuation of derivative
trades with collateralization, counterparty credit gap risk, and funding costs,
following the approach first proposed by Pallavicini and co-authors in 2011.
Based on the risk-neutral pricing principle, we derive a general pricing
equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA,
DVA, LVA and FVA) are introduced by simply modifying the payout cash-flows of
the deal. Funding costs and specific close-out procedures at default break the
bilateral nature of the deal price and render the valuation problem a
non-linear and recursive one. CVA and FVA are in general not really additive
adjustments, and the risk for double counting is concrete. We introduce a new
adjustment, called a Non-linearity Valuation Adjustment (NVA), to address
double-counting. The theoretical risk free rate disappears from our final
equations. The framework can be tailored also to CCP trading under initial and
variation margins, as explained in detail in Brigo and Pallavicini (2014). In
particular, we allow for asymmetric collateral and funding rates, replacement
close-out and re-hypothecation. The valuation equation takes the form of a
backward stochastic differential equation or semi-linear partial differential
equation, and can be cast as a set of iterative equations that can be solved by
least-squares Monte Carlo. We propose such a simulation algorithm in a case
study involving a generalization of the benchmark model of Black and Scholes
for option pricing. Our numerical results confirm that funding risk has a
non-trivial impact on the deal price, and that double counting matters too. We
conclude the article with an analysis of large scale implications of
non-linearity of the pricing equations.Comment: An updated version of this report will appear in the volume:
Veronesi, P. (Editor), \Handbook in Fixed-Income Securities, Wiley, 201
Higgs form factors in Associated Production
We further develop a form factor formalism characterizing anomalous
interactions of the Higgs-like boson (h) to massive electroweak vector bosons
(V) and generic bilinear fermion states (F). Employing this approach, we
examine the sensitivity of pp -> F ->Vh associated production to physics beyond
the Standard Model, and compare it to the corresponding sensitivity of h -> V F
decays. We discuss how determining the Vh invariant-mass distribution in
associated production at LHC is a key ingredient for model-independent
determinations of h V F interactions. We also provide a general discussion
about the power counting of the form factor's momentum dependence in a generic
effective field theory approach, analyzing in particular how effective theories
based on a linear and non-linear realization of the SU(2)_L x U(1)_Y gauge
symmetry map into the form factor formalism. We point out how measurements of
the differential spectra characterizing h -> V F decays and pp -> F -> Vh
associated production could be the leading indication of the presence of a
nonlinear realization of the SU(2)_L x U(1)_Y gauge symmetry.Comment: 21 pages, 14 figures v2: jhep versio
NLIE for hole excited states in the sine-Gordon model with two boundaries
We derive a nonlinear integral equation (NLIE) for some bulk excited states
of the sine-Gordon model on a finite interval with general integrable boundary
interactions, including boundary terms proportional to the first time
derivative of the field. We use this NLIE to compute numerically the dimensions
of these states as a function of scale, and check the UV and IR limits
analytically. We also find further support for the ground-state NLIE by
comparison with boundary conformal perturbation theory (BCPT), boundary
truncated conformal space approach (BTCSA) and the boundary analogue of the
Luscher formula.Comment: 31 pages, LaTeX; graphicx, epstopdf, 4 figure
A Collection of Challenging Optimization Problems in Science, Engineering and Economics
Function optimization and finding simultaneous solutions of a system of
nonlinear equations (SNE) are two closely related and important optimization
problems. However, unlike in the case of function optimization in which one is
required to find the global minimum and sometimes local minima, a database of
challenging SNEs where one is required to find stationary points (extrama and
saddle points) is not readily available. In this article, we initiate building
such a database of important SNE (which also includes related function
optimization problems), arising from Science, Engineering and Economics. After
providing a short review of the most commonly used mathematical and
computational approaches to find solutions of such systems, we provide a
preliminary list of challenging problems by writing the Mathematical
formulation down, briefly explaning the origin and importance of the problem
and giving a short account on the currently known results, for each of the
problems. We anticipate that this database will not only help benchmarking
novel numerical methods for solving SNEs and function optimization problems but
also will help advancing the corresponding research areas.Comment: Accepted as an invited contribution to the special session on
Evolutionary Computation for Nonlinear Equation Systems at the 2015 IEEE
Congress on Evolutionary Computation (at Sendai International Center, Sendai,
Japan, from 25th to 28th May, 2015.
Nonlinear non-extensive approach for identification of structured information
The problem of separating structured information representing phenomena of
differing natures is considered. A structure is assumed to be independent of
the others if can be represented in a complementary subspace. When the
concomitant subspaces are well separated the problem is readily solvable by a
linear technique. Otherwise, the linear approach fails to correctly
discriminate the required information. Hence, a non extensive approach is
proposed. The resulting nonlinear technique is shown to be suitable for dealing
with cases that cannot be tackled by the linear one.Comment: Physica A, in pres
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