New Algorithms for Solving Tropical Linear Systems

The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although counterexamples for existing pseudopolynomial algorithms are (and have to be) very complex. In this work, we continue the study of algorithms for solving tropical linear systems. First, we present a new reformulation of Grigoriev's algorithm that brings it closer to the algorithm of Akian, Gaubert, and Guterman; this lets us formulate a whole family of new algorithms, and we present algorithms from this family for which no known superpolynomial counterexamples work. Second, we present a family of algorithms for solving overdetermined tropical systems. We show that for weakly overdetermined systems, there are polynomial algorithms in this family. We also present a concrete algorithm from this family that can solve a tropical linear system defined by an $m\times n$ matrix with maximal element $M$ in time $\Theta\left({m \choose n} \mathrm{poly}\left(m, n, \log M\right)\right)$, and this time matches the complexity of the best of previously known algorithms for feasibility testing.Comment: 17 page

Bounds on the number of connected components for tropical prevarieties

For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−

Sudden To Adiabatic Transition in Beta Decay

We discuss effects in beta decays at very low beta energies, of the order of the kinetic energies of atomic electrons. As the beta energy is lowered the atomic response changes from sudden to adiabatic. As a consequence, the beta decay rate increases slightly and the ejection of atomic electrons (shake off) and subsequent production of X rays is turned off. We estimate the transition energy and the change in decay rate. The rate increase is largest in heavy atoms, which have a small Q value in their decay. The X ray switch-off is independent of Q value.Comment: 6 pages LaTe

Initiation of Psychotropic Medication after Partner Bereavement: A Matched Cohort Study

Background Recent changes to diagnostic criteria for depression in DSM-5 remove the bereavement exclusion, allowing earlier diagnosis following bereavement. Evaluation of the potential effect of this change requires an understanding of existing psychotropic medication prescribing by non-specialists after bereavement. Aims To describe initiation of psychotropic medication in the first year after partner bereavement. Methods In a UK primary care database, we identified 21,122 individuals aged 60 and over with partner bereavement and no psychotropic drug use in the previous year. Prescribing (anxiolytic/hypnotic, antidepressant, antipsychotic) after bereavement was compared to age, sex and practice matched controls. Results The risks of receiving a new psychotropic prescription within two and twelve months of bereavement were 9.5% (95% CI 9.1 to 9.9%) and 17.9% (17.3 to 18.4%) respectively; an excess risk of initiation in the first year of 12.4% compared to non-bereaved controls. Anxiolytic/hypnotic and antidepressant initiation rates were highest in the first two months. In this period, the hazard ratio for initiation of anxiolytics/hypnotics was 16.7 (95% CI 14.7 to 18.9) and for antidepressants was 5.6 (4.7 to 6.7) compared to non-bereaved controls. 13.3% of those started on anxiolytics/hypnotics within two months continued to receive this drug class at one year. The marked variation in background family practice prescribing of anxiolytics/hypnotics was the strongest determinant of their initiation in the first two months after bereavement. Conclusion Almost one in five older people received a new psychotropic drug prescription in the year after bereavement. The early increase and trend in antidepressant use after bereavement suggests some clinicians did not adhere to the bereavement exclusion, with implications for its recent removal in DSM-5. Family practice variation in use of anxiolytics/hypnotics suggests uncertainty over their role in bereavement with the potential for inappropriate long term use

In ICU state anxiety is not associated with posttraumatic stress symptoms over six months after ICU discharge: A prospective study

Background: Posttraumatic stress symptoms are common after intensive care treatment. The influence of anxiety during critical illness on the development of posttraumatic stress symptoms needs to be investigated. Objective: To determine the association between anxiety during critical illness (state and trait components) and posttraumatic stress symptoms over six months after ICU discharge. Methods: Prospective study including 141 patients admitted ≥24. h to a closed mixed adult ICU in a tertiary hospital. State anxiety was assessed with the Faces Anxiety Scale during ICU stay. Trait anxiety was measured with the State-Trait Anxiety Inventory Form Y-2. Posttraumatic stress symptoms were measured at three and six months after ICU discharge using the Post-Traumatic Stress Symptoms 10-Question Inventory. Clinical and demographical data were also collected. Mixed effect regression models were used to determine if state and trait anxiety were factors significantly associated with posttraumatic stress symptoms over time. Results: Moderate to severe levels of state anxiety in ICU were reported by 81 (57%) participants. Levels of trait anxiety (median 36 IQR: 29-47) were similar to the Australian population. High levels of posttraumatic stress symptoms occurred at three (n = 19, 19%) and six months (n = 15, 17%). Factors independently associated with posttraumatic stress symptoms were trait anxiety (2.2; 95% CI, 0.3-4.1; p = 0.02), symptoms of anxiety after ICU discharge (0.6; 95% CI, 0.2-1.1; p = 0.005), younger age (-1.4; 95% CI, -2.6 to -0.2; p = 0.02) and evidence of mental health treatment prior to the ICU admission (5.2; 95% CI, 1.5-8.9; p = 0.006). Conclusions: Posttraumatic stress symptoms occurred in a significant proportion of ICU survivors and were significantly associated with higher levels of trait anxiety, younger age, mental health treatment prior to the ICU admission and more symptoms of anxiety after ICU discharge. Early assessment and interventions directed to reduce state and trait anxiety in ICU survivors may be of benefit

Depressive symptoms in spouses of older patients with severe sepsis

OBJECTIVE: To examine whether spouses of patients with severe sepsis are at increased risk for depression independent of the spouse's presepsis history, whether this risk differs by sex, and is associated with a sepsis patient's disability after hospitalization. DESIGN: Prospective longitudinal cohort study. SETTING: Population-based cohort of U.S. adults over 50 yrs old interviewed as part of the Health and Retirement Study (1993-2008). PATIENTS: Nine hundred twenty-nine patient-spouse dyads comprising 1,212 hospitalizations for severe sepsis. MEASUREMENTS AND MAIN RESULTS: Severe sepsis was identified using a validated algorithm in Medicare claims. Depression was assessed with a modified version of the Center for Epidemiologic Studies Depression Scale. All analyses were stratified by gender. The prevalence of substantial depressive symptoms in wives of patients with severe sepsis increased by 14 percentage points at the time of severe sepsis (from 20% at a median of 1.1 yrs presepsis to 34% at a median of 1 yr postsepsis) with an odds ratio of 3.74 (95% confidence interval: 2.20, 6.37), in multivariable regression. Husbands had an 8 percentage point increase in the prevalence of substantial depressive symptoms, which was not significant in multivariable regression (odds ratio 1.90, 95% confidence interval 0.75, 4.71). The increase in depression was not explained by bereavement; women had greater odds of substantial depressive symptoms even when their spouse survived a severe sepsis hospitalization (odds ratio 2.86, 95% confidence interval 1.06, 7.73). Wives of sepsis survivors who were disabled were more likely to be depressed (odds ratio 1.35 per activities of daily living limitation of sepsis survivor, 95% confidence interval 1.12, 1.64); however, controlling for patient disability only slightly attenuated the association between sepsis and wives' depression (odds ratio 2.61, 95% confidence interval 0.93, 7.38). CONCLUSIONS: Older women may be at greater risk for depression if their spouse is hospitalized for severe sepsis. Spouses of patients with severe sepsis may benefit from greater support and depression screening, both when their loved one dies and when their loved one survives.NIH K08 HL091249/HL/NHLBI NIH HHS/United States KL2 RR025015-05/RR/NCRR NIH HHS/United States R01 AG030155/AG/NIA NIH HHS/United States U01 AG09740/AG/NIA NIH HHS/United StatesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/93628/1/12.Davydow.CCM.Sepsis.Spouses.pd

Clinicians' perceptions of rationales for rehabilitative exercise in a critical care setting: A cross-sectional study

Australian College of Critical Care Nurses Ltd. Background: Rehabilitative exercise for critically ill patients may have many benefits; however, it is unknown what intensive care unit (ICU) clinicians perceive to be important rationale for the implementation of rehabilitative exercise in critical care settings. Objective: To identify which rationales for rehabilitative exercise interventions were perceived by ICU clinicians to be important and determine whether perceptions were consistent across nursing, medical and physiotherapy clinicians. Methods: A cross-sectional study was undertaken among clinicians (nursing, medical, physiotherapy) working in a mixed medical surgical ICU in an Australian metropolitan tertiary hospital. Participants completed a customised web-based questionnaire developed by a clinician working-group. The questionnaire consisted of 11 plausible rationales for commencing rehabilitative exercise in ICUs based on prior literature and their own clinical experiences grouped into 4 over-arching categories (musculoskeletal, respiratory, psychological and facilitation of discharge). Participants rated their perceived importance for each potential rationale on a 5-point Likert scale. Results: Participants (n = 76) with a median (interquartile range) 4.8 (1.5, 15.5) years of experience working in ICUs completed the questionnaire. Responses were consistent across professional disciplines. Clinicians rated rehabilitative exercise as either 'very much' or 'somewhat' important for facilitating discharge (n = 76, 100%), reducing muscle atrophy (n = 76, 100%), increasing muscle strength (n = 76, 100%), prevention of contractures (n = 73, 96%), reducing the incidence of ICU acquired weakness (n = 62, 82%), increasing oxygenation (n = 71, 93%), facilitating weaning (n = 72, 97%), reducing anxiety (n = 60, 80%), reducing depression (n = 64, 84%), reducing delirium (n = 53, 70%), and increasing mental alertness (n = 65, 87%). Conclusions: Any shortcoming in implementation of rehabilitation exercise is unlikely attributable to a lack of perceived importance by nursing, medical or physiotherapy clinicians who are the most likely clinicians to influence rehabilitation practices in ICUs. It is noteworthy that this study examined self-reported perceptions, not physiological or scientific legitimacy of rationales, or clinician behaviours in practice