Subset Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset Sum on dense instances, proving that Be...

Let $$\mathbb {K}$$ be an uncountable field of characteristic zero and let f a function from {K}^n$$ to . We show that if the restriction every affine plane $$L\subset \mathbb is regular, then regular function.

Intrusion detection systems are designed to provide security in computer networks, so that if the attacker crosses other security devices, they can detect and prevent the attack process. One of the most essential challenges in designing these systems is the so called curse of dimensionality. Therefore, in order to obtain satisfactory performance in these systems we have to take advantage of app...

In this paper we solve an open problem concerning the characterization of those measurable sets $\Omega\subset \mathbb{R}^{2d}$ that, among all having a prescribed Lebesgue measure, can trap largest possible energy fraction in time-frequency space, where density generic function $f\in L^2(\mathbb{R}^d)$ is defined terms its Short-time Fourier transform (STFT) $\mathcal{V} f(x,\omega)$, with Gau...

We present a system which translates sentences from a subset of German into a database. This database w i l l function as the basis for a question-ans-

To evaluate the fully automated FACSCanto software, we compared lymphocyte subpopulation counts obtained using three-color FACSCalibur-CELLQuest and six-color FACSCanto-FACSCanto software techniques. High correlations were observed between data obtained with these techniques. Our study indicated that FACSCanto clinical software is accurate and sensitive in single-platform lymphocyte immunopheno...

Let m + n particles be thrown randomly, independently of each other into N cells, using the following two-stage procedure. 1. The first m particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is 1/N . Let the ith cell contain mi particles on completion. Then associate with this cell the probability ai = mi/m and withdraw the particles. 2. ...

This paper provides the measure theoretic basis for a theory of possibilistic processes. We generalize the definition of a product τ field to an indexed family of τ -fields, without imposing an ordering on the index set. We also introduce the notion ‘measurable cylinder’ and show that any product τ -field can be generated by its associated field of measurable cylinders. Furthermore, we introduc...

Let Fq be the finite field of q elements. Let H ⊆ Fq be a multiplicative subgroup. For a positive integer k and element b ∈ Fq, we give a sharp estimate for the number of k-element subsets of H which sum to b.

In this paper, we obtain an explicit formula for the number of zero-sum k-element subsets in any finite abelian group.