Complexity Results for Modal Dependence Logic

Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfibility for poor man's dependence logic, the language consisting of formulas built from literals and dependence atoms using conjunction, necessity and possibility (i.e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend V\"a\"an\"anen's language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satistiability is complete for the second level of the polynomial hierarchy. In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Approximation of holomorphic mappings on strongly pseudoconvex domains

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a complex Banach manifold. When D is the unit disc in C (or any other topologically trivial strongly pseudoconvex domain in a Stein manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with n=dim Y. Analogous results hold for maps which are holomorphic in D and of class C^r up to the boundary for any positive integer r. We also establish the Oka property for sections of continuous or smooth fiber bundles over the closure of D which are holomorphic over D and whose fiber enjoys the Convex approximation property. The main analytic technique used in the paper is a method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with control up to the boundary, which was developed in our paper "Holomorphic curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)

VASABI: Hierarchical User Profiles for Interactive Visual User Behaviour Analytics

User behaviour analytics (UBA) systems offer sophisticated models that capture users’ behaviour over time with an aim to identify fraudulent activities that do not match their profiles. Making decisions based on such systems; however, requires an in-depth understanding of user behaviour both at an individual and at a group level where a group can consist of users with similar roles. We present a visual analytics approach to help analysts gain a comprehensive, multifaceted understanding of user behaviour at multiple levels. We take a user-centred approach to design a visual analytics framework supporting the analysis of collections of users and the numerous sessions of activities they conduct within digital applications. The framework is centred around the concept of hierarchical user profiles, where the profiles are built based on features derived from sessions they perform and visualised with task-informed designs to facilitate interactive exploration and investigation. We also present techniques to extract user tasks that summarise the behaviour and to cluster users according to these tasks for providing hierarchical overviews of groups of users along with individual users and the sessions they conduct. We externalise a series of analysis goals and tasks, and evaluate our methods through a number of use cases that demonstrate how these tasks are addressed. We observe that with the aid of interactive visual hierarchical user profiles, analysts were able to conduct exploratory and investigative analysis effectively, and able to understand the characteristics of user behaviour to make informed decisions whilst evaluating suspicious users and activities

Analysis of lysine recognition and specificity of the Bacillus subtilis L box riboswitch

The ever-changing environment of a bacterial cell requires sophisticated mechanisms to adjust gene expression in response to changes in nutrient availability. L box riboswitch RNAs regulate gene expression in response to cellular lysine (lys) concentrations in the absence of additional regulatory factors. In Bacillus subtilis, binding of lysine (lys) to the L box RNA causes premature transcription termination in the leader region upstream of the lysC coding sequence. To date, little is known about the specific RNA–lys interactions required for transcription termination. In this study, we characterize features of the B. subtilis lysC leader RNA responsible for lys specificity, and structural elements of the lys molecule required for recognition. The wild-type lysC leader RNA can recognize and discriminate between lys and lys analogs. We identified leader RNA variants with mutations in the lys-binding pocket that exhibit changes in the specificity of ligand recognition. These data demonstrate that lysC leader RNA specificity is the result of recognition of ligand features through a series of distinct interactions between lys and nucleotides that comprise the lys-binding pocket, and provide insight into the molecular mechanisms employed by L box riboswitch RNAs to bind and recognize lys

The lawyer's role in treaty-making: a review : Philip C. Jessup and Howard J. Taubenfeld, Controls for outer space and the Antarctic analogy Louis Henkin, Arms control and inspection in American law

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66554/2/10.1177_002200276000400209.pd

Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations

We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S. Fokas to solve initial-boundary value problems for linear and integrable nonlinear partial differential equations via an extension of the inverse scattering transform. The method takes advantage of the Lax pair formulation for both linear and nonlinear equations, and is based on the simultaneous spectral analysis of both parts of the Lax pair. A key role is also played by the global algebraic relation that couples all known and unknown boundary values. Even though additional technical complications arise in discrete problems compared to continuum ones, we show that a similar approach can also solve initial-boundary value problems for linear and integrable nonlinear differential-difference equations. We demonstrate the method by solving initial-boundary value problems for the discrete analogue of both the linear and the nonlinear Schrodinger equations, comparing the solution to those of the corresponding continuum problems. In the linear case we also explicitly discuss Robin-type boundary conditions not solvable by Fourier series. In the nonlinear case we also identify the linearizable boundary conditions, we discuss the elimination of the unknown boundary datum, we obtain explicitly the linear and continuum limit of the solution, and we write down the soliton solutions.Comment: 41 pages, 3 figures, to appear in Inverse Problem

Ethnic differences in early onset multimorbidity and associations with health service use, long-term prescribing, years of life lost, and mortality: A cross-sectional study using clustering in the UK Clinical Practice Research Datalink

BACKGROUND: The population prevalence of multimorbidity (the existence of at least 2 or more long-term conditions [LTCs] in an individual) is increasing among young adults, particularly in minority ethnic groups and individuals living in socioeconomically deprived areas. In this study, we applied a data-driven approach to identify clusters of individuals who had an early onset multimorbidity in an ethnically and socioeconomically diverse population. We identified associations between clusters and a range of health outcomes. METHODS AND FINDINGS: Using linked primary and secondary care data from the Clinical Practice Research Datalink GOLD (CPRD GOLD), we conducted a cross-sectional study of 837,869 individuals with early onset multimorbidity (aged between 16 and 39 years old when the second LTC was recorded) registered with an English general practice between 2010 and 2020. The study population included 777,906 people of White ethnicity (93%), 33,915 people of South Asian ethnicity (4%), and 26,048 people of Black African/Caribbean ethnicity (3%). A total of 204 LTCs were considered. Latent class analysis stratified by ethnicity identified 4 clusters of multimorbidity in White groups and 3 clusters in South Asian and Black groups. We found that early onset multimorbidity was more common among South Asian (59%, 33,915) and Black (56% 26,048) groups compared to the White population (42%, 777,906). Latent class analysis revealed physical and mental health conditions that were common across all ethnic groups (i.e., hypertension, depression, and painful conditions). However, each ethnic group also presented exclusive LTCs and different sociodemographic profiles: In White groups, the cluster with the highest rates/odds of the outcomes was predominantly male (54%, 44,150) and more socioeconomically deprived than the cluster with the lowest rates/odds of the outcomes. On the other hand, South Asian and Black groups were more socioeconomically deprived than White groups, with a consistent deprivation gradient across all multimorbidity clusters. At the end of the study, 4% (34,922) of the White early onset multimorbidity population had died compared to 2% of the South Asian and Black early onset multimorbidity populations (535 and 570, respectively); however, the latter groups died younger and lost more years of life. The 3 ethnic groups each displayed a cluster of individuals with increased rates of primary care consultations, hospitalisations, long-term prescribing, and odds of mortality. Study limitations include the exclusion of individuals with missing ethnicity information, the age of diagnosis not reflecting the actual age of onset, and the exclusion of people from Mixed, Chinese, and other ethnic groups due to insufficient power to investigate associations between multimorbidity and health-related outcomes in these groups. CONCLUSIONS: These findings emphasise the need to identify, prevent, and manage multimorbidity early in the life course. Our work provides additional insights into the excess burden of early onset multimorbidity in those from socioeconomically deprived and diverse groups who are disproportionately and more severely affected by multimorbidity and highlights the need to ensure healthcare improvements are equitable

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets