Let {Σα}α<ω1 , where ω1 is the first non-countable ordinal, denote the Borel hierarchy of subsets of the Cantor space 2. As usual, Πα denotes the dual class for Σα while ∆ 0 α = Σ 0 α ∩Πα — the corresponding ambiguous class. Let B = ∪α<ω1Σα denote the class of all Borel sets. The levels of Borel hierarchy, as well as many other classes of interest for descriptive set theory, may be defined by m...

Using a highly resolved Long Term Ecological Research (LTER) database collected near Palmer Station, Antarctica, from 1991 to 1994, the variability in the column photosynthetic cross section (ψ*, m 2 g Chl a ) was analyzed. The relationship between the daily integrated primary production rates versus the product of surface irradiance (QPAR(0*)) and the integrated chlorophyll content (down to 0....

We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on average or even at all times, and moreover that any game is linearly equivalent to one in which this is the case. Conversely, we provide conditions under whic...

In this paper, we construct a combination HS-Litehorn of the Halpern-Shoham interval temporal logic HS [15] with the description logic DL-Litehorn [12, 1], which is a Horn extension of the standard language OWL 2 QL. The temporal operators of HS are of the form 〈R〉 (‘diamond’) and [R] (‘box’), where R is one of Allen’s interval relations After, Begins, Ends, During, Later, Overlaps and their in...

We discuss a generalization of Parikh’s Theorem for contextfree languages to classes of many-sorted relational structures which are both definable in Monadic Second Order Logic and which are of bounded patch-width. Patch-width is a generalization of both tree-width and clique-width. This gives a powerful unifying tool to prove that certain classes of graphs are of unbounded width. For R. Parikh...

Ultrasonography uses multiple piezo-electric element probes to image tissues. Current time-domain beamforming techniques require the signal at each transducer-element to be sampled at a rate higher than the Nyquist criterion, resulting in an extensive amount of data to be received, stored and processed. In this work, we propose to exploit sparsity of the signal received at each transducer-eleme...

Let D ≡ 7 mod 8 be a positive squarefree integer, and let hD be the ideal class number of ED = Q( √−D). Let d ≡ 1 mod 4 be a squarefree integer relatively prime to D. Then for any integer k ≥ 0 there is a constant M = M(k), independent of the pair (D, d), such that if (−1)k = sign(d), (2k + 1, hD) = 1, and √ D > 12 π d(log |d|+ M(k)), then the central L-value L(k + 1, χ D,d ) > 0. Furthermore, ...