dataesr/scientific-paragraphs-categorization huggingface dataset:
Seasonal and Spatial Coherence As well as considering a 3° × 3° region around SGP, a 10° × 10° (260-270°E, 32-42°N) region and a 20° × 20° (255-275°E, 30-50°N) region are also used for quantifying the magnitude of the T2M bias during the different months of the simulations. As before, mountainous regions where the NOAA-QCLCD reconstruction is deemed unreliable are excluded from the comparison. Figure  5  shows box and whisker plots of the 5th, 25th, 50th, 75th, and 95th percentiles of the T2M bias for these three different size regions for each month from April to August and for each of the models when considering data from day 2 to day 5. All the models have a median that is too warm during at least one of the months, even over the large 20° × 20° region, although there is significant variability and the 25th to 75th percentiles of the bias across the models span the range from -3 to +10 K.
Maps of Significant T2M Bias The magnitude and spatial extent of the warm bias is now quantified by calculating the day 2 to day 5 mean T2M bias for each 1°× 1° grid box for the nine models that provided gridded data (Figure  7 ). Given that there is a 4 day mean associated with each of the simulations starting on each of the days from April to August, a Student t test is then performed on each 1° × 1° grid box to check whether any biases are significantly different from zero, at the 95% confidence level, and insignificant results are masked out by being shown as white regions. All the models have a statistically significant warm bias over parts of the American Midwest, and this bias covers the region of north Oklahoma and southern Kansas near the SGP ARM site where additional observations were taken as part of the MC3E campaign.
Representativeness of the Bias at SGP A question remains as to how representative the SGP site is of the warm bias occurring across the Midwest. Indeed, this impacts how useful detailed analyses performed using data from SGP are likely to be in understanding the causes of the bias occurring over a wider region. It is possible to calculate the correlation coefficient between the diurnal cycle of the mean bias at SGP and the diurnal cycle of the bias at all other locations (each of them being expressed in terms of local time). The locations where there is a warm bias in ERA-Interim are again marked with upward pointing triangle and crosses, using the same distinction as in Figure  13  (but white symbols are used for clarity due to the different color scale). As the correlations are only calculated where a significant bias in T2M is found in the first place then Figure  14  shows that in all the models, there are a numerous locations with a warm or warm and warming bias with either no bias in ERA-Interim (no white symbol) or a model bias at 00Z that is larger than it is in the analyses (white triangle).
The observations collected at SGP can help in understanding the reasons for the bias there, and there is a large degree of correlation between the T2M bias over large portions of the Midwest and the bias at SGP. Consequently, conclusions about which physical processes contribute to the creation of the bias, drawn from the detailed studies using data at SGP, are likely to reflect model issues prevalent over a much wider area. An analysis of the surface energy balance at SGP in the CMIP5 models showed that errors in both the evaporative fraction and the net downward shortwave contributed to the T2M bias there. In the CMIP5 models, an underestimated latent heat flux and overestimated sensible heat flux led to too much energy being used to warm the surface layer rather than being used to evaporate water  (Zhang et al.
, 2008; Wang et al. , 2015; Zhang & McFarlane, 1995)  that better represents convection initiation due to low tropospheric inhomogeneity, and (3) a probability distribution function (PDF) consistent GFS-TaiESM-Sundqvist macrophysics scheme,  (Wang et al. 2016, in prep; Shiu et al. 2016, in prep) , which removes several ad hoc assumptions of the CAM5 scheme  (Park et al. , 2014) , such as the critical relative humidity for cloud formation. The TaiESM used in the CAUSES project uses the aerosol package setup of the CAM5. 3  (Neale et al. , 2012). These simulations were done on a latitude/ longitude grid with a grid size of 0. 9 by 1. 25°. respectively.
The planetary boundary layer is treated as in  Abdella and McFarlane (1996)  &  Abdella and McFarlane (1997) , modified as described in von  Salzen et al. (2013). Radiation parameterizations include a correlated-k distribution radiative transfer scheme  (Li & Barker, 2005)  and radiative transfer in the presence of clouds using the Monte Carlo independent column approximation  (Barker et al. , 2008). CanAM4 uses a prognostic bulk aerosol scheme with a full sulfur cycle, along with organic and black carbon, mineral dust, and sea salt  (Croft et al. , 2005; Lohmann et al. , 1999). CanCM4 hindcasts are initialized from model runs that assimilate 6-hourly atmospheric temperature, winds and specific humidity using a variant of the incremental analysis update method  (Merryfield et al. , 2013). Initial values of land surface variables for the hindcasts are determined from the response of CLASS in these assimilating model runs without any further data constraints on the land surface.
A8. CNRM: CNRM-CM Two model configurations were run by the Centre National de Recherches Météorologiques (CNRM). The first set of simulations use CNRM-AM6-DIA, which is very close to the landatmosphere component of the CNRM-CM5. 1 climate model  (Voldoire et al. , 2013). Compared to the CNRM-CM5. 1 land-atmosphere component, the model code was updated to version 6. 2. 1 for the atmospheric model ARPEGE-Climat and to version 7. 3 for the land surface model SURFEX  (Masson et al. , 2013) , while keeping the same physical packages in the two models as those used in the CMIP5 exercise. These physical packages are described in detail in  Voldoire et al. (2013). The long-wave radiation scheme is based on the Rapid Radiation Transfer Model  (Mlawer et al. , 1997)  included in the ECMWF IFS model.
, 2002). Unlike the other models, which were initialized from ERA-Interim, the data from CNRM-NWP were produced by the operational model running at the time. Hence, both the atmospheric and soil initial states come from the operational NWP system, which includes soil moisture assimilation  (Giard & Bazile, 2000). The model uses a horizontal resolution of T798 with a stretching factor of 2. 2. This leads to a horizontal resolution of about 10 km over France, 55 km over Australia, and about 20 km near the SGP ARM site.
10 and CRU TS 3. 1) are used for precipitation correction in WFD and WFDEI (see Sect. 3. 1. 2 or  Weedon et al. , 2014a). The precipitation difference between the two CRU datasets is relatively small, while the CMA dataset increases the precipitation to a large extent, by 37. 3 %, compared to CRU for the upper Tarim Basin (Table 3). The changes mostly occur during summer when the peak of CMA precipitation is more than twice as large as precipitation in CRU. The shape of the annual cycle changes greatly as the timing of the peak is shifted from April to July. However, the precipitation amount in winter (DJF) decreases   in CMA, to which the decrease in snowfall is the major contributor. The changes in rainfall and snowfall are similar in all three headwater catchments (Table  3 ) and the upper Tarim Basin.
The modification of the snow and soil freezing scheme increases the trend ratio in the upper Aksu River up to 0. 72, while slightly decreasing it for the two other catchments. In brief, the gradual refinement of the forcing datasets (from WFD-CRU to WFDEI-CRU to WFDEI-CMA to 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 Figure  6. The interannual cycle and intra-annual series of the discharge simulation for three headwater catchments and the upper Tarim Basin: (a, b) Yarkand River, (c, d) Hotan River, (e, f) Aksu River and (g, h) the upper Tarim Basin. Observed discharge for each subbasin was aggregated by the measurements at separated discharge gauges and shown as the black solid line. The simulated discharges at the corresponding grids were extracted from each experiment and plotted as the color lines with markers.
Research on deductive verification of probabilistic programs has considered expectation-based logics, where pre-and post-conditions are real-valued functions on states, and assertion-based logics, where pre-and post-conditions are boolean predicates on state distributions. Both approaches have developed over nearly four decades, but they have different standings today. Expectation-based systems have managed to formalize many sophisticated case studies, while assertion-based systems today have more limited expressivity and have targeted simpler examples. We present Ellora, a sound and relatively complete assertion-based program logic, and demonstrate its expressivity by verifying several classical examples of randomized algorithms using an implementation in the EasyCrypt proof assistant. Ellora features new proof rules for loops and adversarial code, and supports richer assertions than existing program logics.
These limitations raise two points. Compared to expectation-based approaches: 1. Can assertion-based approaches achieve similar expressivity? 2. Are there situations where assertion-based approaches are more suitable? In this paper, we give positive evidence for both of these points. 8 Towards the first point, we give a new assertion-based logic Ellora for probabilistic programs, overcoming limitations in existing probabilistic program logics. Ellora supports a rich set of assertions that can express concepts like expected values and probabilistic independence, and novel proof rules for verifying loops and adversarial code. We prove that Ellora is sound and relatively complete. Towards the second point, we evaluate Ellora in two ways. First, we define a new logic for proving probabilistic independence and distribution law propertieswhich are difficult to capture with expectation-based approaches-and then embed it into Ellora.
This sub-logic is more narrowly focused than Ellora, but supports more concise reasoning for the target assertions. Our embedding demonstrates that the assertion-based approach can be flexibly integrated with intuitive, special-purpose reasoning principles. To further support this claim, we also provide an embedding of the Union Bound logic, a program logic for reasoning about accuracy bounds  [4]. Then, we develop a full-featured implementation of Ellora in the EasyCrypt theorem prover and exercise the logic by mechanically verifying a series of complex randomized algorithms. Our results suggest that the assertion-based approach can indeed be practically viable. Abstract logic. To ease the presentation, we present Ellora in two stages. First, we consider an abstract version of the logic where assertions are general predicates over distributions, with no compact syntax.
To address these issues, we flesh out a concrete version of Ellora. Assertions are described by a grammar modeling a two-level assertion language. The first level contains state predicates-deterministic assertions about a single memory-while the second layer contains probabilistic predicates constructed from probabilities and expected values over discrete distributions. While the concrete assertions are theoretically less expressive than their counterparts in the abstract logic, they can already encode common properties and notions from existing proofs, like probabilities, expected values, distribution laws and probabilistic independence. Our assertions can express theorems from probability theory, enabling sophisticated reasoning about probabilistic concepts. Furthermore, we leverage the concrete syntax to simplify verification.
-We develop an automated procedure for generating pre-conditions of nonlooping commands, inspired by expectation-based systems. -We give syntactic conditions for the closedness and termination properties required for soundness of the loop rules. Implementation and case studies. We implement Ellora on top of Easy-Crypt, a general-purpose proof assistant for reasoning about probabilistic programs, and we mechanically verify a diverse collection of examples including textbook algorithms and a randomized routing procedure. We develop an Easy-Crypt formalization of probability theory from the ground up, including tools like concentration bounds (e. g. , the Chernoff bound), Markov's inequality, and theorems about probabilistic independence. Embeddings. We propose a simple program logic for proving probabilistic independence.
Programs and Assertions Now, we introduce our core programming language and its denotational semantics. Programs. We base our development on pWhile, a strongly-typed imperative language with deterministic assignments, probabilistic assignments, conditionals, loops, and an abort statement which halts the computation with no result. Probabilistic assignments x $ ← g assign a value sampled from a distribution g to a program variable x. The syntax of statements is defined by the grammar: s ::= skip | abort | x ← e | x $ ← g | s; s | if e then s else s | while e do s | x ← I(e) | x ← A(e) where x, e, and g range over typed variables in X , expressions in E and distribution expressions in D respectively. The set E of well-typed expressions is defined inductively from X and a set F of function symbols, while the set D of well-typed distribution expressions is defined by combining a set of distribution symbols S with expressions in E.
When these techniques apply, they can be a convenient and powerful tool. pe(s1; s2, E[ẽ]) = pe(s1, pe(s2, E[ẽ])) pe(x ← e, E[ẽ]) = E[ẽ][x := e] pe(x $ ← g, E[ẽ]) = P g x (E[ẽ]) pe(if e then s1 else s2, E[ẽ]) = pe(s1, E[ẽ]) |e + pe(s2, E[ẽ]) |¬e pc(s, p1 p2) = pe(s, p1) pe(s, p2) To capture this intuitive style of reasoning, researchers have considered lightweight program logics where the assertions and proof rules are tailored to a specific proof technique. We demonstrate how to integrate these tools in an assertion-based logic by introducing and embedding a new logic for reasoning about independence and distribution laws, useful properties when analyzing randomized algorithms. We crucially rely on the rich assertions in Ellora-it is not clear how to extend expectation-based approaches to support similar, lightweight reasoning.
Such assertions are already expressible in the logic of Ellora; adding conditional independence would significantly broaden the scope of the IL proof system and open the possibility to rely on axiomatizations of conditional independence (e. g. , based on graphoids  [33] ). Second, the logic only supports sampling from binomial distributions. It is possible to enrich the language of assertions with clauses c ∼ g where g can model other distributions, like the uniform distribution or the Laplace distribution. The main design challenge is finding a core set of useful facts about these distributions. Enriching the logic and automating the analysis are interesting avenues for further work.
Implementation and Mechanization We have built a prototype implementation of Ellora within EasyCrypt  [5, 2] , a theorem prover originally designed for verifying cryptographic protocols. Easy-Crypt provides a convenient environment for constructing proofs in various Hoare logics, supporting interactive, tactic-based proofs for manipulating assertions and allowing users to invoke external tools, like SMT-solvers, to discharge proof obligations. EasyCrypt provides a mature set of libraries for both data structures (sets, maps, lists, arrays, etc. ) and mathematical theorems (algebra, real analysis, etc. ), which we extended with theorems from probability theory. We used the implementation for verifying many examples from the literature, including all the programs presented in § 7 as well as some additional examples (such as polynomial identity test, private running sums, properties about random walks, etc.
Example A New Library for Probabilistic Independence. In order to support assertions of the concrete program logic, we enhanced the standard libraries of EasyCrypt, notably the ones dealing with big operators and sub-distributions. Like all EasyCrypt libraries, they are written in a foundational style, i. e. they are defined instead of axiomatized. A large part of our libraries are proved formally from first principles. However, some results, such as concentration bounds, are currently declared as axioms. Our formalization of probabilistic independence deserves special mention. We formalized two different (but logically equivalent) notions of independence. The first is in terms of products of probabilities, and is based on heterogenous lists. Since Ellora (like EasyCrypt) has no support for heterogeneous lists, we use a smart encoding based on second-order predicates.
Owing to their richer assertions, program logics are a more suitable foundation for specialized reasoning principles than expectation-based systems. As evidence, our program logic can be smoothly extended with custom reasoning for probabilistic independence and union bounds. Future work includes proving better accuracy bounds for differentially private algorithms, and exploring further integration of Ellora into EasyCrypt. F O(η) ρ µ = F O( η ρ µ ) Fig. 16. Semantics of assertions pe(s, o(p)) = o(pe(s, p)) where o ∈ Ops pe(skip, E[ẽ]) = E[ẽ] pe(s1; s2, E[ẽ]) = pe(s1, pe(s2, E[ẽ])) pe(x ← e, E[ẽ]) = E[ẽ][x := e] pe(x $ ← g, E[ẽ]) = P g x (E[ẽ]) pe(if e then s1 else s2, E[ẽ]) = pe(s1, E[ẽ]) |e + pe(s2, E[ẽ]) |¬e pe(abort, E[ẽ]) = 0 pc(s, p1 p2) = pe(s, p1) pe(s, p2) pc(s, F O(η)) = F O(pc(s, η)) Fig.
The algorithm proceeds by maintaining a current cover (initially empty) and considering each edge in order. If neither endpoint is in current cover, the algorithm adds one of the two endpoints uniformly at random. The Ellora program is: proc VC (E : set<edge>) : var set<node> C ← ∅; for (e1 ,e2 ) in E do if (e1 / ∈ C) ∧ (e2 / ∈ C) then b $ ← {0,1}; C ← (b ? e1 : e2 ) ∪ C; fi end Here, we represent edges as a finite set of pairs of nodes. We loop through the edges, adding one point of each uncovered edge to the cover C uniformly at random. The operator b ? e 1 : e 2 returns e 1 if b is true, and e 2 if not. To prove the approximation guarantee, we first assume that we have a set of nodes C *. We only assume that C * is a valid vertex cover; i. e. , each edge has at least one endpoint in C *.
The PACBO algorithm Since direct sampling from the Gibbs quasi-posterior is usually not possible, we focus on a stochastic approximation in this section, called PACBO (available in the companion eponym R package from  Li, 2016). Both implementation and convergence (towards the Gibbs quasi-posterior) of this scheme are discussed. This section also includes a short numerical experiment on synthetic data to illustrate the potential of PACBO compared to other popular clustering methods.
Batch clustering setting A large variety of methods have been proposed in the literature for selecting the number k of clusters in batch clustering (see  Gordon, 1999; Milligan and    1985, for a survey). These methods may be of local or global nature. For local methods, at each step, each cluster is either merged with another one, split in two or remains. Global methods evaluate the empirical distortion of any clustering as a function of the number k of cells over the whole dataset, and select the minimizer of this distortion. The rule of  Hartigan (1975)  is a well-known representative of local methods. Popular global methods include the works of  Calinski and Harabasz (1974) ,  Krzanowski and Lai (1988)  and  Kaufman and Rousseeuw (1990) , where functions based on the empirical distortion or on the average of within-cluster dispersion of each point are constructed and the optimal number of clusters is the maximizer of these functions.
Online clustering setting In the last part, we have compared, in the batch setting, our method with 7 other methods on different datasets. However let us stress here that none of the aforementioned methods is specifically designed for online clustering. Indeed, to the best of our knowledge PACBO is the sole procedure that explicitly takes advantage of the sequential nature of data. For that reason, we present below the behavior and a comparison of running times between PACBO and the aforementioned methods, on the following synthetic online clustering toy example. Model 5 (10 mixed groups in dimension 2). Observations (x t ) t=1,. ,T=200 are simulated in the following way: define firstly for each t ∈ 1, T a pair (c 1,t , c 2,t ) ∈ R 2 , where c 1,t = -5 2 π + 5π 9 t-1 20 -1 and c 2,t = 5 sin(c 1,t ).
READEX leverages the hardware features for Dynamic Voltage and Frequency Scaling (DVFS) of the Intel Haswell processor family that allows the userspace governor to set the frequency for individual cores as opposed to full sockets as seen in previous processor lines. In addition, the frequency of the uncore chip area can be tuned in the Haswell processor independent of the core frequency. 4 The frequencies can be controlled by setting machine specific registers (MSRs). The READEX methodology is a two-stage approach and consists of Design Time Analysis (DTA) and Runtime Application Tuning (RAT). DTA applies an auto-tuning approach to compute best system configurations for instances of program regions, called runtime situations (rts ′ s). Different runtime situations of a region are identified in the READEX methodology by region identifiers, eg, the call path of the given instance.
It describes how domain knowledge, such as the program regions and the phase region (Section 4. 1. 1), application characteristics (Section 4. 2), and the ATP (Section 4. 3) specifications can be added by the application expert. Section 5 provides details on the implementation of the identifiers and the ATPs and how DTA uses the domain knowledge to generate a more refined tuning model. The static and dynamic energy savings obtained after applying region identifiers for the Multi-Grid (MG) benchmark from the NAS parallel benchmark suite  9  are discussed in Section 6. 1, followed by a description on the trend in the energy consumption for the multi-zone version of the Block Tri-diagonal solver (BT) for different input sets in Section 6. 2. An evaluation of the results obtained for the ESPRESO library 10 using preconditioners, domain decomposition, and iterative solver switching as the Application Tuning Parameters is also presented in Section 6.
DESIGN-TIME ANALYSIS DTA is implemented using the Periscope Tuning Framework (PTF) that was developed at the Technical University of Munich, Germany. PTF is a distributed framework consisting of the frontend, the tuning plugins, the experiment execution engine, and a hierarchy of analysis agents. 6 PTF provides several tuning plugins for different tuning aspects, such as energy consumption and compiler flags. A tuning plugin determines a number of system configurations based on expert knowledge and then assesses the configurations via experiments that measure the objective function. A novel tuning plugin called the READEX Tuning Plugin was developed for PTF to perform DTA by running experiments that currently evaluate three tuning parameters, ie, CPU frequency, uncore frequency, and the number of OpenMP threads within a single program run.