We prove Weak Borisov--Alexeev--Borisov Conjecture in dimension three which states that the anti-canonical volume of an $\epsilon$-klt log Fano pair is bounded from above.

We reduce here end-point estimates for one singular operator (namely for dyadic square function) to Monge–Ampère equations with drift. The spaces are weighted spaces, and therefore the domain, where we solve our PDE is non-convex. If we are in the end-point situation our goal is either to find a logarithmic blow-up of the norm estimate from below, or to prove that there is upper estimate of the...

Defining a feasible notion of space over the Blum-Shub-Smale (BSS) model of algebraic computation is a long standing open problem. In an attempt to define a right notion of space complexity for the BSS model, Naurois [CiE, 2007] introduced the notion of weak-space. We investigate the weak-space bounded computations and their plausible relationship with the classical space bounded computations. ...

a log-domain current-mode true rms-to-dc converter based on a novel synthesis of a simplified current-mode low pass filter and a two-quadrant squarer/divider is presented. the circuit employs floating gate mos (fg-mos) transistors operating in weak inversion region. the converter features low power(<1.5uw), low supply voltage (0.9v), two quadrant input current, immunity from body effect, low ci...

We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that #CSP(F) is in FP if F is weakly log-m...

In the Local Computation Algorithms (LCA) model, the algorithm is asked to compute a part of the output by reading as little as possible from the input. For example, an LCA for coloring a graph is given a vertex name (as a “query”), and it should output the color assigned to that vertex after inquiring about some part of the graph topology using “probes”; all outputs must be consistent with the...

It’s easy to check that any specific string of length n has probability at most (1 − δ), hence SV-sources are n log 1 1−δ -sources. Also recall that SV-sources are (k, l) block sources where k = l log 1 1−δ . Suppose δ = log 1 1−δ , then k = δl. Take a hash-based extractor E : {0, 1} × {0, 1} → {0, 1}. Here, our weak-source is a SVsource over the strings of length n and suppose k = n log 1 1−δ ...

We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the light-trails technology. We give two online algorithms which we prove to have competitive ratios O(log n) and O(log n) respectively. We also consider a simplification of the problem in which the communication pattern is fixed and known before hand, for which we give a solutio...

Rare and Weak models for multiple hypothesis testing assume that only a small proportion of the tested hypotheses concern non-null effects individual are moderately large, so they generally do not stand out individually, example in Bonferroni analysis. Such have been studied quite few settings, some cases studies focused on an underlying Gaussian means model being tested; others, Poisson Binomi...