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This work investigates an alternative model for neural machine translation (NMT) and proposes a novel architecture, where we employ a multi-dimensional long short-term memory (MDLSTM) for translation modeling. In the state-of-the-art…
A complex projective tower or simply a $\mathbb CP$-tower is an iterated complex projective fibrations starting from a point. In this paper we classify all 6-dimensional $\mathbb CP$-towers up to diffeomorphism, and as a consequence, we…
The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric information. It is defined via the Serre construction by an abelian surface in P1 x P3. The…
We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group $G$. Topological order in 2+1d is known to be characterized in terms of modular tensor categories (MTCs),…
We study when two projective bundles over two arbitrary smooth projective varieties of different dimensions can be isomorphic. We show that two multi-projective bundles (fibre product of projective bundles) over different projective spaces…
The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of…
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…
A real Bott tower is obtained as the orbit space of the $n$-torus $T^n$ by the free action of an elementary abelian 2-group $(\mathbb{Z}_2)^n$. This paper deals with the classification of 5-dimensional real Bott towers and study certain…
We consider the structure of roller coaster permutations as introduced by Ahmed & Snevily[1]. A roller coaster permutation is described as a permuta- tion that maximizes the total switches from ascending to descending or visa versa for the…
We show how the spellings of known words can help us deal with unknown words in open-vocabulary NLP tasks. The method we propose can be used to extend any closed-vocabulary generative model, but in this paper we specifically consider the…
We intend to generate low-dimensional explicit distributional semantic vectors. In explicit semantic vectors, each dimension corresponds to a word, so word vectors are interpretable. In this research, we propose a new approach to obtain…
The support vector machine (SVM) is a well-established classification method whose name refers to the particular training examples, called support vectors, that determine the maximum margin separating hyperplane. The SVM classifier is known…
For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a_b_c_d_..._e, parenthesized either from the bottom upwards…
Text-to-level generation aims to translate natural language descriptions into structured game levels, enabling intuitive control over procedural content generation. While prior text-to-level generators are typically limited to a single game…
This paper explores a new perspective on the universality of the vertical lift in tangent categories by presenting a categorification of the dimension of smooth manifolds. The universality of the vertical lift is a key part of the axioms of…
In this paper, we proved that there exist four distinct diffeomorphism classes of three-dimensional real Bott tower $M(A)=(S^1)^3/(\mathbb{Z}_2)^3$, and 12 distinct diffeomorphism classes of four-dimensional real Bott tower…
Neural Machine Translation (NMT) models generally perform translation using a fixed-size lexical vocabulary, which is an important bottleneck on their generalization capability and overall translation quality. The standard approach to…
Recent years have seen remarkable advances in the field of Simultaneous Machine Translation (SiMT) due to the introduction of innovative policies that dictate whether to READ or WRITE at each step of the translation process. However, a…
If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in…
Low pole order frames of slanted vector fields are constructed on the space of vertical k-jets of the universal family of complete intersections in $\mathbb{P}^n$ and, adapting the arguments, low pole order frames of slanted vector fields…