Given a graph G = (V, E), we define the transpose degree sequence d T j to be equal to the number of vertices of degree at least j. We define L G , the graph Laplacian, to be the matrix, whose rows and columns are indexed by the vertex set V , whose diagonal entry at v is the degree of v and whose value at a pair (v, w) is −1 if (v, w) ∈ E and 0 otherwise. Grone and Merris conjectured [GM] Conj...

In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β >...

Analysis of dissolved light hydrocarbon gas concentrations (primarily methane and ethane) in water supply wells is commonly used to establish conditions before and after drilling in areas of shale gas and oil extraction. Several methods are currently used to collect samples for dissolved gas analysis from water supply wells; however, the reliability of results obtained from these methods has no...

Often, when dealing with real-world recognition problems, we do not need, and often cannot have, knowledge of the entire set possible classes that might appear during operational testing. In such cases, need to think robust classification methods able deal "unknown" properly reject samples belonging never seen training. Notwithstanding, existing classifiers date were mostly developed for closed...

We give a C0051JUCtion for new families of semi-regular divisible difference sets. The construction iJ a variation of McFarland's scheme [Sl tor nonc;yclic difference SCIS. • Let G be a group of order 11111 and N a subgroup of G of order n. If D is a k-subset of G then Dis a {m, n, le , >.1, >.2) divisible difference set in G relative to N provided that the differences dd'1 fur d, d ' ED, d ;e ...

开放环境下的模式识别与文字识别应用中，新数据、新模式和新类别不断涌现，要求算法具备应对新类别模式的能力。针对这一问题，研究者们开始聚焦开放集文字识别（open-set text recognition，OSTR）任务。该任务要求，算法在测试（推断）阶段，既能识别训练集见过的文字类别，还能够识别、拒识或发现训练集未见过的新文字。开放集文字识别逐步成为文字识别领域的研究热点之一。本文首先对开放集模式识别技术进行简要总结，然后重点介绍开放集文字识别的研究背景、任务定义、基本概念、研究重点和技术难点。同时，针对开放集文字识别三大问题（未知样本发现、新类别识别和上下文信息偏差），从方法的模型结构、特点优势和应用场景的角度对相关工作进行了综述。最后，对开放集文字识别技术的发展趋势和研究方向进行了分析展望。;Text recognition is focused on transcription-...

In traditional semantic segmentation, knowing about all existing classes is essential to yield effective results with the majority of approaches. However, these methods trained in a Closed Set fail when new are found test phase, not being able recognize that an unseen class has been fed. This means they suitable for Open scenarios, which very common real-world computer vision and remote sensing...