2,922 research outputs found
Fractional differentiability for solutions of nonlinear elliptic equations
We study nonlinear elliptic equations in divergence form
When
has linear growth in , and assuming that enjoys smoothness, local
well-posedness is found in for certain values of
and . In the particular case
, and ,
, we obtain for each
. Our main tool in the proof is a more general result, that
holds also if has growth in , , and
asserts local well-posedness in for each , provided that
satisfies a locally uniform condition
Nonlocal properties of entangled two-photon generalized binomial states in two separate cavities
We consider entangled two-photon generalized binomial states of the
electromagnetic field in two separate cavities. The nonlocal properties of this
entangled field state are analyzed by studying the electric field correlations
between the two cavities. A Bell's inequality violation is obtained using an
appropriate dichotomic cavity operator, that is in principle measurable.Comment: 5 pages, 1 figur
Exploring Cognitive States: Methods for Detecting Physiological Temporal Fingerprints
Cognitive state detection and its relationship to observable physiologically telemetry has been utilized for many human-machine and human-cybernetic applications. This paper aims at understanding and addressing if there are unique psychophysiological patterns over time, a physiological temporal fingerprint, that is associated with specific cognitive states. This preliminary work involves commercial airline pilots completing experimental benchmark task inductions of three cognitive states: 1) Channelized Attention (CA); 2) High Workload (HW); and 3) Low Workload (LW). We approach this objective by modeling these "fingerprints" through the use of Hidden Markov Models and Entropy analysis to evaluate if the transitions over time are complex or rhythmic/predictable by nature. Our results indicate that cognitive states do have unique complexity of physiological sequences that are statistically different from other cognitive states. More specifically, CA has a significantly higher temporal psychophysiological complexity than HW and LW in EEG and ECG telemetry signals. With regards to respiration telemetry, CA has a lower temporal psychophysiological complexity than HW and LW. Through our preliminary work, addressing this unique underpinning can inform whether these underlying dynamics can be utilized to understand how humans transition between cognitive states and for improved detection of cognitive states
Solution of the Lindblad Equation in the Kraus Representation
The so-called Lindblad equation, a typical master equation describing the
dissipative quantum dynamics, is shown to be solvable for finite-level systems
in a compact form without resort to writing it down as a set of equations among
matrix elements. The solution is then naturally given in an operator form,
known as the Kraus representation. Following a few simple examples, the general
applicability of the method is clarified.Comment: 9 page
On the Performance Prediction of BLAS-based Tensor Contractions
Tensor operations are surging as the computational building blocks for a
variety of scientific simulations and the development of high-performance
kernels for such operations is known to be a challenging task. While for
operations on one- and two-dimensional tensors there exist standardized
interfaces and highly-optimized libraries (BLAS), for higher dimensional
tensors neither standards nor highly-tuned implementations exist yet. In this
paper, we consider contractions between two tensors of arbitrary dimensionality
and take on the challenge of generating high-performance implementations by
resorting to sequences of BLAS kernels. The approach consists in breaking the
contraction down into operations that only involve matrices or vectors. Since
in general there are many alternative ways of decomposing a contraction, we are
able to methodically derive a large family of algorithms. The main contribution
of this paper is a systematic methodology to accurately identify the fastest
algorithms in the bunch, without executing them. The goal is instead
accomplished with the help of a set of cache-aware micro-benchmarks for the
underlying BLAS kernels. The predictions we construct from such benchmarks
allow us to reliably single out the best-performing algorithms in a tiny
fraction of the time taken by the direct execution of the algorithms.Comment: Submitted to PMBS1
Machine-assisted Cyber Threat Analysis using Conceptual Knowledge Discovery
Over the last years, computer networks have evolved into highly dynamic and interconnected environments, involving multiple heterogeneous devices and providing a myriad of services on top of them. This complex landscape has made it extremely difficult for security administrators to keep accurate and be effective in protecting their systems against cyber threats. In this paper, we describe our vision and scientific posture on how artificial intelligence techniques and a smart use of security knowledge may assist system administrators in better defending their networks. To that end, we put forward a research roadmap involving three complimentary axes, namely, (I) the use of FCA-based mechanisms for managing configuration vulnerabilities, (II) the exploitation of knowledge representation techniques for automated security reasoning, and (III) the design of a cyber threat intelligence mechanism as a CKDD process. Then, we describe a machine-assisted process for cyber threat analysis which provides a holistic perspective of how these three research axes are integrated together
Using Strategy Improvement to Stay Alive
We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides
solving an MPG in the usual sense, our algorithm computes more information
about the game, information that is important with respect to applications. The
weights of the edges of an MPG can be thought of as a gained/consumed energy --
depending on the sign. For each vertex, our algorithm computes the minimum
amount of initial energy that is sufficient for player Max to ensure that in a
play starting from the vertex, the energy level never goes below zero. Our
algorithm is not the first algorithm that computes the minimum sufficient
initial energies, but according to our experimental study it is the fastest
algorithm that computes them. The reason is that it utilizes the strategy
improvement technique which is very efficient in practice
23, 25, 26-trihydroxycholecalciferol. A 25-hydroxycholecalciferol-26,23-lactone precursor
(23S)-1,23,25-Trihydroxycholecalciferol, an intestinal metabolite of 1,25-dihydroxycholecalciferol
Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas
In recent work we have shown how it is possible to define very precise type
systems for object-oriented languages by abstractly compiling a program into a
Horn formula f. Then type inference amounts to resolving a certain goal w.r.t.
the coinductive (that is, the greatest) Herbrand model of f.
Type systems defined in this way are idealized, since in the most interesting
instantiations both the terms of the coinductive Herbrand universe and goal
derivations cannot be finitely represented. However, sound and quite expressive
approximations can be implemented by considering only regular terms and
derivations. In doing so, it is essential to introduce a proper subtyping
relation formalizing the notion of approximation between types.
In this paper we study a subtyping relation on coinductive terms built on
union and object type constructors. We define an interpretation of types as set
of values induced by a quite intuitive relation of membership of values to
types, and prove that the definition of subtyping is sound w.r.t. subset
inclusion between type interpretations. The proof of soundness has allowed us
to simplify the notion of contractive derivation and to discover that the
previously given definition of subtyping did not cover all possible
representations of the empty type
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