On the Hardness of Energy Minimisation for Crystal Structure Prediction

Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as "NP-Hard and very challenging" without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of csp with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the csp removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of csp. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.Comment: Short version published in SOFSEM 2020, full version to be published in Fundamenta Informatica

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models

We Study the low-temperature thermodynamical and statistical properties of the ASYNNNI model, used to describe oxygen ordering in YBa2Cu3O6+2c. Analyzing the excited states we show that this model undergoes a second order phase transition at absolute zero temperature, From the divergence of the relative energy fluctuations, in the limit T -- GT 0, we deduce that for T approximate to 0 the deviation of the chemical potential it from its ground state value is linearly related to the partial derivative of the fraction of threefold coordinated Cu(1) ions it with respect to oxygen concentlation c. We use the cluster variation method (CVM) to determine the numerical value of the coefficient of this, relation and find that it is equal to - 1/2, independently of the values of the interaction parameters. This establishes a full equivalence between the ASYNNNI model and the one-dimensional Ising model, where the role of the nearest-neighbor interaction of the latter is played by the V-2 interaction in the former. We comment on the general applicability of low levels of the CVM approximation to systems equivalent to the one-dimensional Ising model

Postoperative adjuvant chemotherapy in rectal cancer operated for cure

BACKGROUND: Colorectal cancer is one of the most common types of cancer in the Western world. Apart from surgery - which remains the mainstay of treatment for resectable primary tumours - postoperative (i.e., adjuvant) chemotherapy with 5-fluorouracil (5-FU) based regimens is now the standard treatment in Dukes' C (TNM stage III) colon tumours i.e. tumours with metastases in the regional lymph nodes but no distant metastases. In contrast, the evidence for recommendations of adjuvant therapy in rectal cancer is sparse. In Europe it is generally acknowledged that locally advanced rectal tumours receive preoperative (i.e., neoadjuvant) downstaging by radiotherapy (or chemoradiotion), whereas in the US postoperative chemoradiotion is considered the treatment of choice in all Dukes' C rectal cancers. Overall, no universal consensus exists on the adjuvant treatment of surgically resectable rectal carcinoma; moreover, no formal systematic review and meta-analysis has been so far performed on this subject. OBJECTIVES: We undertook a systematic review of the scientific literature from 1975 until March 2011 in order to quantitatively summarize the available evidence regarding the impact of postoperative adjuvant chemotherapy on the survival of patients with surgically resectable rectal cancer. The outcomes of interest were overall survival (OS) and disease-free survival (DFS). SEARCH METHODS: CCCG standard search strategy in defined databases with the following supplementary search. 1. Rect* or colorect* - 2. Cancer or carcinom* or adenocarc* or neoplasm* or tumour - 3. Adjuv* - 4. Chemother* - 5. Postoper* SELECTION CRITERIA: Randomised controlled trials (RCT) comparing patients undergoing surgery for rectal cancer who received no adjuvant chemotherapy with those receiving any postoperative chemotherapy regimen. DATA COLLECTION AND ANALYSIS: Two authors extracted data and a third author performed an independent search for verification. The main outcome measure was the hazard ratio (HR) between the risk of event between the treatment arm (adjuvant chemotherapy) and the control arm (no adjuvant chemotherapy). The survival data were either entered directly in RevMan or extrapolated from Kaplan-Meier plots and then entered in RevMan. Due to expected clinical heterogeneity a random effects model was used for creating the pooled estimates of treatment efficacy. MAIN RESULTS: A total of 21 eligible RCTs were identified and used for meta-analysis purposes. Overall, 16,215 patients with colorectal cancer were enrolled, 9,785 being affected with rectal carcinoma. Considering patients with rectal cancer only, 4,854 cases were randomized to receive potentially curative surgery of the primary tumour plus adjuvant chemotherapy and 4,367 to receive surgery plus observation. The mean number of patients enrolled was 466 (range: 54-1,243 cases). 11 RCTs had been performed in Western countries and 10 in Japan. All trials used fluoropyrimidine-based chemotherapy (no modern drugs - such as oxaliplatin, irinotecan or biological agents - were tested).Overall survival (OS) data were available in 21 RCTs and the data available for meta-analysis regarded 9,221 patients: of these, 4854 patients were randomized to adjuvant chemotherapy (treatment arm) and 4,367 patients did not receive adjuvant chemotherapy (control arm). The meta-analysis of these RCTs showed a significant reduction in the risk of death (17%) among patients undergoing postoperative chemotherapy as compared to those undergoing observation (HR=0.83, CI: 0.76-0.91). Between-study heterogeneity was moderate (I-squared=30%) but significant (P=0.09) at the 10% alpha level.Disease-free survival (DFS) data were reported in 20 RCTs, and the data suitable for meta-analysis included 8,530 patients. Of these, 4,515 patients were randomized to postoperative chemotherapy (treatment arm) and 4,015 patients received no postoperative chemotherapy (control arm). The meta-analysis of these RCTs showed a reduction in the risk of disease recurrence (25%) among patients undergoing adjuvant chemotherapy as compared to those undergoing observation (HR=0.75, CI: 0.68-0.83). Between-study heterogeneity was moderate (I-squared=41%) but significant (P=0.03).While analyzing both OS and DFS data, sensitivity analyses did not find any difference in treatment effect based on trial sample size or geographical region (Western vs Japanese). Available data were insufficient to investigate on the effect of adjuvant chemotherapy separately in different TNM stages in terms of both OS and DFS. No plausible source of heterogeneity was formally identified, although variability in treatment regimens and TNM stages of enrolled patients might have played a significant role in the difference of reported results. AUTHORS' CONCLUSIONS: The results of this meta-analysis support the use of 5-FU based postoperative adjuvant chemotherapy for patients undergoing apparently radical surgery for non-metastatic rectal carcinoma. Available data do not allow us to define whether the efficacy of this treatment is highest in one specific TNM stage. The implementation of modern anti-cancer agents in the adjuvant setting is warranted to improve the results shown by this meta-analysis. Randomized trials of adjuvant chemotherapy for patients receiving preoperative neoadjuvant therapy are also needed in order to define the role of postoperative chemotherapy in the multimodal treatment of resectable rectal cancer