Jan Kraszewski

On some new ideals on the Cantor and Baire spaces

We define and investigate some new ideals of subsets of the Cantor space and the Baire space. We show that combinatorial properties of these ideals can be described by the splitting and reaping cardinal numbers. We show that there exist perfect Luzin sets for these ideals on the Baire space.

Boosting algorithm with sequence-loss cost function for structured prediction

The problem of sequence prediction i.e annotating sequences appears in many problems across a variety of scientific disciplines, especially in computational biology, natural language processing, speech recognition, etc The paper investigates a boosting approach to structured prediction, AdaBoostSTRUCT, based on proposed sequence-loss balancing function, combining advantages of boosting scheme with the efficiency of dynamic programming method In the paper the methods formalism for modeling and predicting label sequences is introduced as well as examined, presenting its validity and competitiveness.

Bernstein sets and k -coverings

䅢stract. In this paper we study a notion of a �-covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We consider also other types of coverings. 1. Definitions and notation In 1993 Car汳on 楮 h楳 paper 嬳] 楮troduced a not楯n of �-cover楮gs and used 楴 for 楮vest楧at楮g whether some 楤ea汳 are or are not �-trans污tab汥. Later on �-cover楮gs were stud楥d by other authors, e⹧. Muthuvel (cf. [7 崩 and Now楫 (cf. 嬸崬 嬹崩. In th楳 paper we present new resu汴s on �-cover楮gs 楮 connect楯n w楴h Bernste楮 sets. We a汳o 楮troduce two natural genera汩zat楯ns of the not楯n of �-cover楮gs, name汹 �-S-cover楮gs and �-I-cover楮gs. We use standard set-theoret楣al notat楯n and term楮o汯gy from [ 1崮 Reca汬 that the card楮a汩ty of the set of a汬 real numbers R 楳 denoted by c. The card楮a汩ty of a set A 楳 denoted by jAj. If � 楳 a card楮al number then