Generating infinite monoids of cellular automata

For a group [Formula: see text] and a set [Formula: see text], let [Formula: see text] be the monoid of all cellular automata over [Formula: see text], and let [Formula: see text] be its group of units. By establishing a characterization of surjunctive groups in terms of the monoid [Formula: see text], we prove that the rank of [Formula: see text] (i.e. the smallest cardinality of a generating set) is equal to the rank of [Formula: see text] plus the relative rank of [Formula: see text] in [Formula: see text], and that the latter is infinite when [Formula: see text] has an infinite decreasing chain of normal subgroups of finite index, condition which is satisfied, for example, for any infinite residually finite group. Moreover, when [Formula: see text] is a vector space over a field [Formula: see text], we study the monoid [Formula: see text] of all linear cellular automata over [Formula: see text] and its group of units [Formula: see text]. We show that if [Formula: see text] is an indicable group and [Formula: see text] is finite-dimensional, then [Formula: see text] is not finitely generated; however, for any finitely generated indicable group [Formula: see text], the group [Formula: see text] is finitely generated if and only if [Formula: see text] is finite.

Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions

We consider an elliptic problem of the type $$\left\{ {\matrix{ {-\Delta u = f(x,u)\quad } \hfill & {{\rm in}\,\Omega } \hfill \cr {u = 0} \hfill & {{\rm on}\,\Gamma _1} \hfill \cr {\displaystyle{{\partial u} \over {\partial \nu }} = g(x,u)} \hfill & {{\rm on}\,\Gamma _2} \hfill \cr } } \right.$$ where Ω is a bounded Lipschitz domain in ℝN with a cylindrical symmetry, ν stands for the outer normal and $\partial \Omega = \overline {\Gamma _1} \cup \overline {\Gamma _2} $.Under a Morse index condition, we prove cylindrical symmetry results for solutions of the above problem.As an intermediate step, we relate the Morse index of a solution of the nonlinear problem to the eigenvalues of the following linear eigenvalue problem $$\left\{ {\matrix{ {-\Delta w_j + c(x)w_j = \lambda _jw_j} \hfill & {{\rm in }\Omega } \hfill \cr {w_j = 0} \hfill & {{\rm on }\Gamma _1} \hfill \cr {\displaystyle{{\partial w_j} \over {\partial \nu }} + d(x)w_j = \lambda _jw_j} \hfill & {{\rm on }\Gamma _2} \hfill \cr } } \right.$$ For this one, we construct sequences of eigenvalues and provide variational characterization of them, following the usual approach for the Dirichlet case, but working in the product Hilbert space L2 (Ω) × L2(Γ2).

ОСОБЛИВОСТІ ДІАГНОСТИКИ СТАНУ ЗДОРОВ'Я ПАЦІЄНТА З ПОЗИЦІЙ МОБІЛЬНОЇ МЕДИЦИНИ. ПОСТАНОВКА ПРОБЛЕМИ

The theoretical aspects of the diagnosis of the patients in mobile medical problems are revised. It is emphasized the idea about the need for comprehensive use of primary examination of patients (complaints, these general and local examination, laboratory and instrumental studies); previous research materials and comprehensive account of the risks and environmental conditions. The necessity of the transition of control of certain physiological parameters to monitor the changes of integral indicators of the condition of the patient is noted. It is postulated that the value of the integral index condition can be defined as the minimum distance between the point of multidimensional space of normalized values of physiological parameters and regions of space that meets the dynamic rate.

Diagnostic Errors that Lead to Inappropriate Antimicrobial Use

OBJECTIVEWe found previously that inappropriate inpatient antimicrobial use was often attributable to erroneous diagnoses. Here, we detail diagnostic errors and their relationship to inappropriate antimicrobial courses.DESIGNRetrospective cohort studySETTINGVeterans Affairs hospitalPATIENTSA cohort of 500 randomly selected inpatients with an antimicrobial courseMETHODSBlinded reviewers judged the accuracy of the initial provider diagnosis for the condition that led to an antimicrobial course and whether the course was appropriate.RESULTSThe diagnoses were correct in 291 cases (58%), incorrect in 156 cases (31%), and of indeterminate accuracy in 22 cases (4%). In the remaining 31 cases (6%), the diagnosis was a sign or symptom rather than a syndrome or disease. The odds ratio of a correct diagnosis was 4.3 (95% confidence interval [CI], 2.2–8.5) if the index condition was related to the reason for admission. When the diagnosis was correct, 181 of 292 courses (62%) were appropriate, compared with only 10 of 208 (5%) when the diagnosis was incorrect or indeterminate or when providers were treating a sign or symptom rather than a syndrome or disease (P<.001). Among the 309 cases in which antimicrobial courses were not appropriate, reasons varied by diagnostic accuracy; in 81 of 111 cases (73%) with a correct diagnosis, incorrect antimicrobial(s) were selected; in 166 of 198 other cases (84%), antimicrobial therapy was not indicated.CONCLUSIONSDiagnostic accuracy is important for optimal inpatient antimicrobial use. Antimicrobial stewardship strategies should help providers avoid diagnostic errors and know when antimicrobial therapy can be withheld safely.Infect Control Hosp Epidemiol 2015;36(8):949–956

Chronic Conditions and Health Problems in Rheumatic Diseases: Comparisons with Rheumatoid Arthritis, Noninflammatory Rheumatic Disorders, Systemic Lupus Erythematosus, and Fibromyalgia

Objectives.To describe and compare the prevalence of lifetime and current self-reported comorbidity and associated quality of life in 4 rheumatic diseases, and to investigate comorbid conditions in light of the overlap between the index condition and comorbid conditions (CC), and in the context of symptom-type diagnoses.Methods.We studied comorbidity in 11,704 patients with fibromyalgia (FM), systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), and noninflammatory rheumatic disorders (NIRD). Patients completed semiannual self-reports relating to 22 present and past illnesses and completed the EuroQol (EQ-5D) utility index.Results.CC were most common in FM, followed by SLE. FM comorbidity was dominated by depression, mental illness, and symptom-type comorbidity (e.g., gastrointestinal and genitourinary disorders). In SLE, there were substantial increases in hypertension, depression, cataract, fractures, and cardiovascular and cerebrovascular, neurologic, lung, gall bladder and endocrine disorders compared with RA. Any current CC reduced the EQ-5D utility by 0.08 to 0.16 units. The lowest EQ-5D score was noted for current psychiatric illness (0.55) and current depression (0.60).Conclusion.Four patterns of comorbidity emerged: that associated with aging; that associated with aging but enhanced by the index condition, as in SLE and cardiovascular disease; comorbidity that is part of the symptoms complex of the index condition; and CC that represent lifetime traits or manifestations of the underlying illness. Depression was the most strongly associated correlate of EQ-5D quality of life, and current depression was present in about 15% of patients with RA or NIRD and 34% to 39% of those with SLE and FM.