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Deductive biocomputing.

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Deductive Biocomputing Jeff Shrager1*, Richard Waldinger2, Mark Stickel2, J. P. Massar3 1 Department of Plant Biology, Carnegie Institution of Washington, Stanford, California, United States of America, 2 Artificial Intelligence Center, SRI International, Menlo Park, California, United States of America, 3 Berkeley, California, United States of America Background. As biologists increasingly rely upon computational tools, it is imperative that they be able to appropriately apply these tools and clearly understand the methods the tools employ. Such tools must have access to all the relevant data and knowledge and, in some sense, ‘‘understand’’ biology so that they can serve biologists’ goals appropriately and ‘‘explain’’ in biological terms how results are computed. Methodology/Principal Findings. We describe a deduction-based approach to biocomputation that semiautomatically combines knowledge, software, and data to satisfy goals expressed in a high-level biological language. The approach is implemented in an open source web-based biocomputing platform called BioDeducta, which combines SRI’s SNARK theorem prover with the BioBike interactive integrated knowledge base. The biologist/user expresses a high-level conjecture, representing a biocomputational goal query, without indicating how this goal is to be achieved. A subject domain theory, represented in SNARK’s logical language, transforms the terms in the conjecture into capabilities of the available resources and the background knowledge necessary to link them together. If the subject domain theory enables SNARK to prove the conjecture—that is, to find paths between the goal and BioBike resources—then the resulting proofs represent solutions to the conjecture/query. Such proofs provide provenance for each result, indicating in detail how they were computed. We demonstrate BioDeducta by showing how it can approximately replicate a previously published analysis of genes involved in the adaptation of cyanobacteria to different light niches. Conclusions/Significance. Through the use of automated deduction guided by a biological subject domain theory, this work is a step towards enabling biologists to conveniently and efficiently marshal integrated knowledge, data, and computational tools toward resolving complex biological queries. Citation: Shrager J, Waldinger R, Stickel M, Massar JP (2007) Deductive Biocomputing. PLoS ONE 2(4): e339. doi:10.1371/journal.pone.0000339 INTRODUCTION Background Biologists must increasingly conduct computational analyses across integrated biological knowledge and data [1], but biologists who cannot program are relegated to searching in knowledge bases and carrying out canned computations that have been programmed by others. To conduct novel computations—ones for which no canned solution exists—biologists often hire programmers, but this is either expensive or hit-and-miss (or both), and usually results in overly specific one-off solutions. Moreover, putting non-biologist programmers between biologists and biocomputation removes the biologist from the details of the computation [2], which makes biologists nervous about the correctness of the results—as well it should. Unlike physics, there is no clear categorization within biology of, for example, theoretical vs. experimental vs. computational biologists whose practitioners could naturally collaborate. As a result, it is often nearly impossible for the authors of papers (usually biologists) to accurately and completely describe the computational methods used to solve a given biological problem. Although this will certainly change as computational techniques become standardized and biologists learn to program—indeed a whole new species called ‘‘computational biologist’’ is rapidly evolving—it would be useful if biologists had ‘‘intelligent’’ tools that, in a sense, ‘‘understand’’ biology, could help the biologists conduct analyses, and could explain how the analyses were accomplished, all expressed in terms that are natural to the biologists. The present paper explores just such an ‘‘intelligent’’ paradigm that we call deductive biocomputing. In our paradigm biologists/users express queries as goals in high-level near-natural terms. Others— usually biologists who are more computationally savvy working with programmers—provide instructions to the platform about how to satisfy those goals. Automatic methods then put these together to satisfy the goals and to explicitly record how the answers were discovered. This is analogous to the widely studied problem of automatic program generation [3,4] in which a specification for a program is expressed in a high-level language and then translated into an actual program that implements the specification. (Although fully general automatic program synthesis is an unsolved problem, the present query resolution problem is more tractable because we are looking for an answer to a specific query, not a procedure that will answer an entire class of queries. In particular, because the inputs to the query are generally known in advance, we can evaluate tests and unwind loops at proof-time, this avoiding having to automatically generate conditional branches and iterative or recursive loops.) Academic Editor: Robert Futrelle, Northeastern University, United States of America Received January 12, 2007; Accepted March 6, 2007; Published April 4, 2007 Copyright: ß 2007 Shrager et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was supported in part by the National Science Foundation, under the Science and Engineering Information Integration and Informatics (SEIII) Program (NSF IIS-0513857), and by a grant from the NASA Advanced Information Systems Research Program through cooperative agreement NO6-4803 between NASA-Ames (Andrew Pohorille P.I.) and The Inst. for the Study of Learning and Expertise. Competing Interests: The authors have declared that no competing interests exist. * To whom correspondence should be addressed. E-mail: jshrager@stanford. edu PLoS ONE | www.plosone.org 1 April 2007 | Issue 4 | e339 Deductive Biocomputing The deductive approach to biocomputation Engineers approach complex knowledge-based goals in three general ways: (a) the ‘‘procedural’’ approach, (b) the ‘‘relational’’ approach, and (c) the ‘‘deductive’’ approach. In the procedural approach (a) one specifies each step required to reach the goal, down to the level at which the steps are primitives in the domain language. Such procedures often involve search in knowledge bases, generally traversing the structures that represent complex knowledge, transforming data, and conducting specific calculations along the way. Usually writing programs of this sort is beyond the skill of biologists. In the relational approach (b) queries are written such that the complex inner loops (searching over records) are implicit; for example: ‘‘Select genes (g1) of organism1 with the word ‘photo- synthesis’ in their annotation field, and where there is a gene (g2) in organism2 such that g1 and g2 are orthologous.’’ Such queries can be directly executed by the relational database engine, thus simplifying the programming process. Still, in order to make use of this approach in complex analyses the biologist must know a great deal about how the knowledge bases are structured, and what tools are available. In the deductive approach (c), the biologist specifies a high-level goal, usually without knowing how it will be satisfied, and a runtime executor (called a theorem prover for reasons that will become clear below) does whatever work is required to satisfy the goal. One might, for example, ask: ‘‘Find photosynthetic orthologs between organism1 and organism2.’’ Whereas the relational approach goes beyond the procedural approach by leaving loop optimization to the computer, the deductive approach goes beyond even the relational approach by avoiding the necessity of describing an algorithm at all. No computation is explicitly described; instead, the query is expressed in declarative, problem-appropriate terms; it is the job of the theorem prover to bridge the gap between the query-level concepts and the computational ones. Leaving method determination to the computer is a significant though difficult advance; whereas the implicit search carried out by the relational database engine requires knowledge of how to execute and optimize a certain class of algorithms (complex loops over relational databases), the deductive approach requires that the computer have additional understanding of how aspects of the knowledge base are connected to one another, and how to use these connections in service of high-level goals. The computer must, in a sense, ‘‘understand’’ how the knowledge is organized, and how it relates to high-level goals. Generally the knowledgebase designer provides such information to the theorem prover in what we shall call a subject domain theory. Rather than representing one-off methods, this knowledge can be expressed modularly so that it can be applied to a wide array of different goals. Through this specification of a subject domain theory and application of a general theorem prover, the end-user biologist—the person at the top who needs the results of the computation to begin with—is relying on the knowledge-base designers and the theorem prover to do the heavy lifting. At the end of this paper we will see that in addition to providing great power to the biologist-user, deductive biocomputing affords a number of significant advantages over either task-specific programs or relational queries, including a coherent way of recording where results come from (called provenance). Also, one can nearly (but not quite) get to true natural language programming, in which the biologist can ask a question in plain language and efficiently obtain both results and a detailed explanation of how they were calculated. But there are also efficiency limitations to this technique, and special requirements in terms of the consistency of the symbols (names) used in the subject domain theory. We will return to these points in the discussion. The core of a deductive approach is the subject domain theory, an ontology comprising definitions of domain concepts, descriptions of the capabilities of available resources including data, knowledge, and tools, and the background knowledge necessary to relate these to high-level queries. While the word ontology is sometimes taken to mean a description of vocabulary and taxonomy of the domain, we mean here a formal axiomatic theory that defines domain concepts and relates them to one another. We use the word axiom to include what is often called a rule in the Semantic Web or Expert Systems literature. We employ full first-order logic as the representation language of the subject domain theory. (Readers familiar with theorem proving technologies will correctly recoil at the undecidability of full first-order logic. We address this issue in some detail in the Discussion section of the paper.)The query, or question to be answered, is also expressed in the language of logic; specifically it is phrased as a conjecture whose validity is to be proved by an automatic proof in the subject domain theory (thus the term theorem prover). The axioms of the subject domain theory allow the query conjecture to be transformed and decomposed into subgoals, leading eventually (one hopes) to a proof. If a proof is found, answerextraction techniques are applied to the proof to yield an answer [3,4]. If more than one proof is found, more than one answer may be extracted. METHOD BioDeducta = SNARK+BioBike While the applicability of the deductive approach is independent of any particular implementation, our prototype implementation, called BioDeducta, is built largely from existing components. The theorem prover is SRI’s reasoner SNARK [5]. The query and subject domain theory are formulated in SNARK’s logical language. SNARK has a procedural-attachment mechanism that allows one to consult external resources while a proof is in progress, and a mechanism for extracting answers to queries from discovered proofs. SNARK uses a ‘‘sorted logic’’, in which each entity bears a syntactic indication of what ‘‘sort’’, or type, of object it is. Biology-specific data, knowledge, and software resources are drawn from the BioBike environment [2], an integrated biological data and knowledge repository and biology-specific programming environment. BioBike provides integrated access to a number of knowledge sources, including the Gene Ontology (GO) [6], Kegg (www.genome.jp/kegg/), a BioCyc Database [7] for Cyanobacteria, and biological literature, as well as important biological software tools such as Meme, BLAST, R, and Clustal. BioBike is built on top of the KnowOS (Knowledge Operating System) [8], which embeds the biological knowledge and data in a frame-based programmable knowledge environment, and provides web-based access to it, as well as the ability to call out to remote resources over the web. The KnowOS includes SNARK as a built-in facility, and SNARK procedural attachments link symbols of the SNARK subject domain theory to BioBike functions. Both SNARK and BioBike are written entirely in Common Lisp, and are offered as open-source freeware. Moreover, there is a fully functional BioBike demo server, including SNARK, on which the examples in this paper can be tested, and wherein users can freely develop new BioDeducta applications of their own design (see www. biobike.org). The ‘‘hli’’ problem We here illustrate the BioDeducta approach with an extended, realistic example. The cyanobacterium subspecies Procholorococ- PLoS ONE | www.plosone.org 2 April 2007 | Issue 4 | e339 Deductive Biocomputing cus is widely distributed in the world’s oceans, and plays a critical role both in the marine ecosystem and in the global carbon cycle [9]. A problem of interest to biologists is how these organisms are adapted to their environmental niches. Bahya et al. [10] studied the genomic differences among many strains of the cyanobacteria with respect to their adaptation to niches of differing levels of light and nutrients. Among the Procholorococci, Procholorococcus sp. strain Med4 (aka. ProMed4 or Med4) is adapted to high light, living in the upper part of the ocean, whereas Procholorococcus sp. strain MIT9313 (aka. Pro9313) is adapted to lower light, living in somewhat deeper waters (although still in the ‘‘euphotic zone’’ where there is some available sunlight). Bhaya et al. were interested in which proteins (and their genes) are involved in this adaptation—that is those one might call the high light adaptive genes of ProMed4. (For simplicity in the present discussion we interchangeably refer to genes, and the RNAs and proteins that they code for. As we are dealing here with bacteria, this simplification is not too problematic, and BioBike knows how to automatically determine when translation is needed between these.) One way to address this biological question is to ask which proteins in ProMed4 have no ortholog—that is, no gene of similar apparent function (based upon sequence similarity)—in Pro9313. One can get an even finer bead on this question by examining microarray expression results for the genes that produce those proteins, asking which of those genes unique to ProMed4 demonstrate a significant light response (for example, are 26 upregulated in a light stress experiment). Unfortunately, microarrays for the Prochlorococci have only recently been developed, so no such experimental work exists. However, there are a number of such studies using the related freshwater cyanobacterium: Synechocystis sp. strain PCC6803 (aka. s6803) [11]. Going one step further, one may focus specifically on the genes that are annotated as photosynthesis-related according to some formalization of gene function, such as the Gene Ontology (GO). In sum, we can expand this question as follows: Which photosynthesis-related proteins in ProMed4 have no ortholog in Pro9313 but do have an ortholog in s6803 such that the genes producing those proteins exhibits a light stress response (greater than 26 ratio in microarray data), and possibly are annotated as light-related genes? One algorithm to find such genes might be: For each photosynthesis-related gene/protein in ProMed4, Find its best protein-level ortholog in Pro9313 and S6803, When there is no Pro9313 ortholog, but there is a S6803 ortholog, and the expression ratio for the genes (mRNAs) that produce the S6803 ortholog are .26 up-regulated in the Hihara microarray dataset, collect the ProMed4 gene/protein. Expressed in the native BioBike language (BioLisp), this might be written as follows: (loop for pm4prot in (#ˆproteins promed4) as 9313ortho = (best-ortholog pm4prot pro9313) as 6803ortho = (best-ortholog pm4prot s6803) when (and (photosynthesis-related pm4prot) (null 9313ortho) 6803ortho (. = (array-select 6803ortho Hihara1) 2.0)) collect pm4prot) Although this solution is concise and relatively efficient, its programming requires detailed knowledge of both the BioLisp programming language, and of how to call upon BioBike’s knowledge resources. Moreover, this is a one-shot solution specific to this particular problem, not affording of significant reuse (i.e., methodological modularity). Nor does this approach get us any more than the solution reported as an opaque answer that cannot be unpacked into the method that solved it (provenance). In contrast to this approach, the BioDeducta methodology allows us to more conveniently express and solve this problem while simultaneously offering methodological modularity and solution provenance. We two cameras = approx. 100 m) and their focus on different marking trees. Outcomes were analysed to support or reject the hypotheses and predictions outlines in Table 1; it is important to note that multiple predictions can be tested through post-hoc subdivision of individual tests and that this does not represent a repeated reanalysis of the dataset with the associated risk of Type I error [59,63]. Association x2 tests were also applied to both scent marking and investigatory behaviour by each age sex class in both the breeding and non-breeding seasons. This allowed for the proportion of scent marking/investigating events to be analysed in relation to the total capture events of each age sex class. frequencies of individuals: present on trails (H = 4.173, df = 3, p = 0.243), marking (H = 4.987, df = 3, p = 0.173) or investigating (H = 4.246, df = 3, p = 0.236). The non-breeding season consisted of a median of 6 events per adult male (n = 17: 1–46), 4 per adult female (n = 9: 2–89), 15.5 per female with young (n = 10: 3–41) and 3 per subadult (n = 9: 1–21). The frequencies of marking by individuals between age sex classes was significantly different during the non-breeding season (H = 8.203, df = 3, p = 0.042). There were insufficient data to conduct pair-wise comparisons to identify the age sex classes contributing to this significance. No significant difference was found between age sex classes in the frequencies of individuals present on trails (H = 6.077, df = 3, p = 0.108) or investigating (H = 4.818, df = 3, p = 0.186). Comparison of frequencies of events at a population level revealed variation in marking and investigatory behaviour as a product of age sex class and season. When using trails containing marking trees, adult males marked trees more than expected across both seasons (Fig. 1 A & B). When using trails, adult females marked less than expected across both seasons (Fig. 1 A & B). No females with young (,1 year of age) were captured on cameras during the breeding season. Females with young (.1 yr during the breeding season; all ages during the non-breeding season) marked and investigated as expected when using trails across both seasons (Fig. 1 A–D). Subadults marked less than expected when using trails during the breeding season (Fig. 1 A), but as expected during the non-breeding season (Fig. 1 B). When using trails, all brown bears investigated marks as expected (Fig. 1 C & D), except adult females, who investigated marks less than expected outside of the breeding season (Fig. 1 D). Results of association tests and the frequency of marking and investigating by each age sex class, within each season, are displayed in Table 5. Adult males were associated with scent marking behaviour significantly more than expected across both seasons. During the non-breeding season, they were more likely to mark a tree than not, when passing on a trail. Adult females were associated with scent marking behaviour significantly less than expected across both seasons. During the non-breeding season, they were more likely not to mark a tree than to mark it, when passing on a trail. Adult females were associated with investigating marks significantly less than expected during the non-breeding season. Subadults were associated with scent marking significantly less than expected during the breeding season. Related outcomes of hypotheses and predictions are outlined in Table 1. Results A total of 1,050 events were captured during the breeding and non-breeding seasons. Classification of images revealed 733 independent camera trap events assigned to age sex class; 694 were also identified to the individual level, and assigned to their unique identifier. A total of 159 behavioural events during the breeding season and 574 during the non-breeding season were documented, and assigned to an age sex class. There were 39 events where individuals could not be identified, all from the nonbreeding season: of these, 8 were adult males, 2 adult females, 22 females with dependent young, and 7 subadults. The individual(s) in 12 events during the breeding season and 67 during the nonbreeding season could not be identified to an age or sex class. The individual(s) captured in 25 events during the breeding season and 252 events during the non-breeding season could not be sexed but were identified as adults. Table 4 displays the number of individuals included in analyses for each age sex class and season. No significant difference was found between the proportion of individuals within each age sex class captured on trails and the general population observed at that time (breeding season: x2 = 0.378, df = 3, p = 0.945; non-breeding season: x2 = 0.761, df = 3, p = 0.859). Therefore the presence of bears on trails was said to be representative of the observed population in the area. The median number of capture events per individual varied by age sex class and according to season. Events during the breeding season consisted of a median capture of 5 events per adult male (n = 7: (min-max) 1–32), 4 per adult female (n = 7: 1–11), 11 per female with young (n = 2: 3–19) and 2.5 per subadult (n = 8: 1–8). No significant difference was found between age sex classes, in the PLoS ONE | www.plosone.org Discussion To our knowledge we are the first to publish data using camera traps to assess scent marking behaviour in wild Ursids, and the first to assess the proportional rate of chemical signalling by different age sex classes of wild brown bears across seasons. Other studies using camera trap images to visually identify carnivores with a relatively uniform pelage report a lower capture success and/or 6 April 2012 | Volume 7 | Issue 4 | e35404 Chemical Signalling in Brown Bears Figure 1. Behavioural frequencies in relation to trail use. Total observed events of marking (A, B) and investigation (C, D) by each age sex class, compared to their expected frequency in relation to their presence on trails containing active marking trees. Comparisons during the breeding (A & C) and non-breeding season (B & D). *** indicates p,0.001 in subdivided testing, ** p,0.01 and * p,0.05. doi:10.1371/journal.pone.0035404.g001 lack the ability to identify between individuals/genders [60,64,65]. Studies using camera traps to capture bears report effort between 493 and 1,200 trap nights [60,66,67], much lower than the sampling intensity employed in this study. The presence of different age sex classes on trails was found to be representative of their proportion in the general population, indicating that this study does not just represent a subset of individuals. The frequency of behaviours shown by each age sex Table 5. x2 for association tests displaying total behavioural events per age sex class for the breeding and non-breeding season. Breeding season Scent marking Marking Investigating Non-marking Investigating Non- Investigating Adult males 38+ 39 17 60 Adult females 72 30 10 27 Females with young 11 11 7 15 Subadults 32 20 7 16 x2 = 17.464, df = 3, p,0.001 x2 = 1.261, df = 3, p = 0.738 Non-breeding season Scent marking Investigating Marking Non-marking Investigating Non-investigating Adult males 70+ 982 33 135 Adult females 112 132+ 122 131 Females with young 71 134 44 161 Subadults 15 43 11 47 x2 = 47.967, df = 3, p,0.001 x2 = 11.105, df = 3, p = 0.011 +/2 indicates significantly more/less than expected (p,0.05). doi:10.1371/journal.pone.0035404.t005 PLoS ONE | www.plosone.org 7 April 2012 | Volume 7 | Issue 4 | e35404 Chemical Signalling in Brown Bears necessarily avoiding productive areas where adults accumulate, but selecting not to mark trees in these areas, subadults may be able to avoid signalling information to adult individuals which may convey competition and prove costly. class can therefore be attributed to the behaviour of the population at that time. Self-advertisement for mate attraction A significant male bias in scent marking behaviour was found during the breeding and non-breeding seasons. Adult males scent marked more than expected in relation to their presence on trails, and were associated with marking more than any other age sex class across both seasons. This continued activity is inconsistent with the self-advertisement for mate attraction hypothesis which predicted that adult males would mark less outside of the breeding season. We also found evidence inconclusive with the male-biased self-advertisement hypothesis in the behaviour of adult females. Adult females did not investigate scent marks more than expected in relation to their presence on trails during the breeding season, nor was investigation positively associated with the age sex class over others. Outside of the breeding season adult females did investigate marking trees less than expected, which could highlight a change in behaviour consistent with the self-advertisement hypothesis. However, without an increase in ✸ Ð ✸ Ð Ð Ð ✸ ß ✸ Ð ✸ ✸ Ð Ð Ð Ð Ð Ð ✸ ✸ ✸ Ð ✸ ❞ ☛✍✆✤☛✖✕✗✩✡☛✖✕✗✑✘☛❂✁✛✥➋ß➡✁☎✞✡✠☞✆✟✞✡✠❅➴❀✓✔➮☎✕✗✢✛✣✤✁✛✥♥✠ ➘ ☛❋✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌❅✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮ ➹ ✢✭❐✟✣✔☛✚✶✳➃✯ ✏ ➴ ✃ ➴☞✠☞☛✖✄ ✁☎✕➎✠ ➘ ☛❋✓✪✕✡✆✟✞✡✠❜➴❀✓✔➮☎✕✗✢✛✣✪➴❀➮❛➀✍✮➪➮✪❻❬✯ ✶ ✶ ➮❛➀ ➹❅➘ ☛◆✆✗✌❀☛✖➴☞☛✖✕✗✑✘☛❜✁✛✥✵✁☎✞✡✠☞✆✟✞✡✠➂➴❀✓✔➮☎✕✗✢✛✣✪❖➴ ß★➴☞☛✖✑✘✌❀☛✍✠☞☛✖✩➈❐ ✃ ✑✘☛✖✣✪✣✪➴✍✮✛Ô ➘ ✁☎➴☞☛❜➮✛☛✖✕✡☛❅✠☞✌✜✢✛✕✒➷ ➴❀✑✘✌✜✓✔✆✗✠❀✓✔✁☎✕➋✌❀☛✍➮☎✞✗✣✪✢✭✠❀✓✔✁☎✕➋✆✗✌❀✁✒✑✘☛✖➴❀➴☞☛✖➴❜✑✘✁✛✌❀✌❀☛✖➴☞✆✤✁☎✕✗✩➋✠☞❱ ✁ ❋❽✶➞✷✰✯✲✱✌✳❽✶☎✹✜✮✡✩✡☛✖➴❀✓✔➮☎✕✗➴❻✠ ➘ ✢✭✠ ✠ ➘ ☛❂❒✟✌✜➴☞✠❅✣✔☛✍✫✛☛✖✣❚✑✘☛✖✣✪✣✪➴❜✁✛✥✧✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌❅✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮➈➴ ✃ ➴☞✠☞☛✖✄ ✌❀☛✖✑✘☛✖✓✔✫✛☛✚✢➈✑✘✁☎✄✚❐✟✓✪✕✗✢✭✠❀✓✔✁☎✕ ✁✛✥✤✠ ➘ ☛❅✓✪✕✡✆✟✞✡✠✧➴❀✓✔➮☎✕✗✢✛✣✪➴❃Ô ➘ ✓✪✑ ➘ ➴❀✢✭✠❀✓✪➴☞✥ ✃ ☎☛ ✳✬ ✞✗✢✭✠❀✓✔✁☎✕★✷❷Ð✬✹✜✯❃⑤ ❢ ✁✛✠☞☛⑤✠ ➘ ✢✭✠➂✠ ➘ ☛❅✑✘✁☎✄✝✆✟✞✡✠❀✢❬➷ ✠❀✓✔✁☎✕➈✆✗✌❀✁✒✑✘☛✖➴❀➴➂✁✛✥➝✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌➂✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮✚✄✝✁✒✩✡☛✖✣✡✥❪✁✛✌✂➴☞✁☎✣✔✫✒✓✪✕✡➮❋✥❪✁✛✌✜✄❉✞✗✣✪✢➈✷❷Ð✬✹➂✑✍✢✛✕➈❐✤☛ ✻✖❝✛✶ ✏✞✡✌❀☛✖✣✪✓✪❳ ✢ ❲➂✌❀✁✭❒✟✌ ✘ ✢✛➴❀➴☞✁✒✑✍✓✪✢✭✠☞☛✖✩➈Ô⑤✓✔✠ ➘ ✢❽❐✟✓✪✕✗✢✭✌ ✃ ✠☞✌❀☛✍☛⑤➴☞✠☞✌✜✞✗✑✘✠❀✞✡✌❀☛❅✑✘✁☎✕✗➴❀✓✪➴☞✠❀✓✪✕✡➮❽✁✛✥✴✻❽✣✔☛✍✫✛☛✖✣✪➴✍✯ ➹❅➘ ☛❜✕✳✞✗✄❺➷ ❐✤☛✍✌❅✁✛✥♥✣✔☛✍✫✛☛✖✣✪➴✚✷❪✠ ➘ ☛❋✩✡☛✍✆✗✠ ➘ ✹✂✩✡☛✍✠☞☛✍✌✜✄➈✓✪✕✡☛✖➴◆✥❪✁✛✌✜✄❉✞✗✣✪✢➎✷❷Ð✬✹❜✑✍✢✛✣✪✑✍✞✗✣✪✢✭✠❀✓✔✁☎✕➞✠❀✓✪✄✝☛✛✯ ➹❅➘ ☛ ✄➈✢✭✠ ➘ ☛✖✄➈✢✭✠❀✓✪✑✍✢✛✣➝✢✛✕✗✩➎➴☞✠☞✁✒✑ ➘ ✢✛➴☞✠❀✓✪✑❂✄✝✁✒✩✡☛✖✣✪➴✂✆✤☛✍✌✜✄➈✓✔✠◆✞✗➴◆✠☞✁✝☛✼▼✤☛✖✑✘✠❀✞✗✢✭✠☞☛✚✕✳✞✗✄✝☛✍✌✜✓✪✑✍✢✛✣ ☛✍✫✭✢✛✣✪✞✗✢✭✠❀✓✔✁☎✕➎✁✛✥❃➮✛☛✖✕✡☛✖➴❅➴☞Ô⑤✓✔✠❀✑ ➘ ✓✪✕✡➮❺✠❀✓✪✄✝☛➈✷❴✑✘✁☎✄✝✆✟✞✡✠❀✢✭✠❀✓✔✁☎✕❛✠❀✓✪✄✝☛❬✹✜✯ ✫ ☛✚✑✍✢✛✕★✑✍✢✛✣✪✑✍✞✒➷ ✣✪✢✭✠☞☛➞✠ ➘ ☛➞✕✡☛✖✑✘☛✖➴❀➴❀✢✭✌ ✃ ✑✘✁☎✄✝✆✟✞✡✠❀✢✭✠❀✓✔✁☎✕ ✠❀✓✪✄✝☛➥✷❴✢✛➴❺✢P✥❴✞✗✕✗✑✘✠❀✓✔✁☎✕➒✁✛✥❅☛✖✕✺✫✒✓✔✌❀✁☎✕✗✄✝☛✖✕✺✠❀✢✛✣ ➴☞✠❀✓✪✄❉✞✗✣✪✓❪✹✜✮✺✓✰✯ ☛✛✯✧✩✗✞✡✌✜✢✭✠❀✓✔✁☎✕➈✓✪✕✝Ô ➘ ✓✪✑ ➘ Ð☎✝✷ ➧➨✾❚➩❼➫❬✹♥✁☎✞✡✠☞✆✟✞✡✠❻➴❀✓✔➮☎✕✗✢✛✣➝✷❴✄✝✁☎✣✔☛✖✑✍✞✗✣✔☛✖❃➴ ♥ß ✹ ➘ ✢✛➴ ✠☞✁➎✢✭✆✗✆✤☛✖✢✭✌❂✓✪✕P✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌✏✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮➌➴ ✃ ➴☞✠☞☛✖✄➎✯ ✫ ☛✝✑✘✁☎✕✗➴❀✓✪✩✡☛✍✌✏✠ ➘ ✢✭✠❽✠ ➘ ☛❉✁☎✞✡✠☞✆✟✞✡✠ ➴❀✓✔➮☎✕✗✢✛✣✪➴❋✢✭✌❀☛➋✸✗✎✷ ➭❼➲❵❙✎➳❭➫❬✹✏✓✔✥❽Ð☎✝✷ ➧➨✾❚➩❼➫❬✹❽➴❀✓✔➮☎✕✗✢✛✣✪➴❂✩✡✁★✕✡✁✛✠✚✢✭✆✗✆✤☛✖✢✭✌✚✓✪✕ ✠ ➘ ☛➈☛✍✫✭✢✛✣✪✞✗✢✭✠☞☛✖✩ ✑✘✁☎✄✝✆✟✞✡✠❀✢✭✠❀✓✔✁☎✕×✠❀✓✪✄✝☛✛✯ ➹❅➘ ☛❛✆✗✌❀✁✛✆✤✁☎➴☞☛✖✩×✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌➋✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮➡✄✝✁✒✩✡☛✖✣❉✷ ➘ ✢✖✫✒✓✪✕✡➮ ✩✡☛✍✆✗✠ ➘ ✻☎✹◆✑✍✢✛✕★✑✍✢✛✣✪✑✍✞✗✣✪✢✭✠☞☛✚✢✝✑✍✣✪✢✛➴❀➴❜✁✛✥♥✆✗✌❀✁✛✆✤✁☎➴❀✓✔✠❀✓✔✁☎✕✗✢✛✣✵✥❪✁✛✌✜✄❉✞✗✣✪✢❺✓✪✕➞✠ ➘ ☛✚✑✘✁☎❭✕ ❬❀✞✗✕✗✑❨➷ ✠❀✓✔✫✛☛✝✕✡✁✛✌✜✄➈✢✛✣❚✥❪✁✛✌✜✄ ✷❴✣✪✓❪✴✛☛❉✥❪✁✛✌✜✄❉✞✗✣✪✢P✷❷Ð✬✹☞✹❅Ô⑤✓✔✠ ➘ ✠⑥Ô✂✁➞✫✭✢✭✌✜✓✪✢✭❐✟✣✔☛✖➴❺✷❴✪✕ ➎❂✻☎✹❅✢✛✕✗✩★✠⑥Ô✂✁ ✑✍✣✪✢✛✞✗➴☞☛✖➴➋✓✪✕✾✠⑥Ô✂✁➡✆✟✢✭✌✜✢✛✣✪✣✔☛✖✣①➷⑥✑✘✁☎✕✗➴☞☛✖✑✍✞✡✠❀✓✔✫✛☛❛➴☞✠☞☛✍✆✟➴➈Ô⑤✓✔✠ ➘ ✆✟✢✭✌✜✢✛✣✪✣✔☛✖✣◆➮☎✢✭✠☞☛✖➴➋✥❴✞✗✣①❒✵✣✪✣✪✓✪✕✡➮ ✣✔✁✛➮☎✓✪✑✍✢✛✣✴✥❴✞✗✕✗✑✘✠❀✓✔✁☎✕✗❇ ➴ ❈❊❉✌✳➔❋✌❈❆ ★✯ ç ➶✜➺ ♦❅➓ ➼ q s ♦ ➼✸è t ❷Ø ✕➥✠ ➘ ✓✪➴❂✆✟✢✭✆✤☛✍✌❋✓✔✠❋✓✪➴❋✢✛➴❀➴❀✞✗✄✝☛✖✩➥✠ ➘ ✢✭✠⑨✯✲✱✌✳✚✮❚✓✰✯ ☛✛✯➈✠ ➘ ☛➈✌❀☛✍➮☎✞✗✣✪✢✭✠❀✓✔✁☎✕➥✆✗✌❀✁✒✑✘☛✖➴❀➴❂✁✛✥ ➮✛☛✖✕✡☛❽✠☞✌✜✢✛✕✗➴❀✑✘✌✜✓✔✆✗✠❀✓✔✁☎✕➌✓✪✕➋✣✪✓✔✫✒✓✪✕✡➮✚✑✘☛✖✣✪✣✪➴✂✄➈✢ ✃ ❐✤☛✏✌❀☛✍✆✗✌❀☛✖➴☞☛✖✕✺✠☞☛✖✩➞✢✛➴◆✢❺✩✡☛✍✠☞☛✍✌✜✄➈✓✪✕✗✓✪➴☞✠❀✓✪✑ ❒✵✕✗✓✔✠☞☛❜✢✛✞✡✠☞✁☎✄➈✢✭✠☞✁☎✕✴❃✯ Ö ✘ ✣✪✓✔✫✒✓✪✕✡➮✏✑✘☛✖✣✪✣✡✓✪➴♥✢✛✕✝☛✘Ú✡✢✛✄✝✆✟✣✔☛◆✁✛✥❼ ❜❈❆❋❅➷➀❐✟✢✛➴☞☛✖✩✝✄✝✁☎✣✔☛✖✑✍✞✗✣✪✢✭✌☞➷ ➮✛☛✖✕✡☛✍✠❀✓✪✑➥✄➈✢✛✑ ➘ ✓✪✕✡☛P✥❴✞✗✣①❒✵✣✪✣✪✓✪✕✡➮➒✣✔✁✛➮☎✓✪✑✍✢✛✣✏✥❴✞✗✕✗✑✘✠❀✓✔✁☎④ ✕ ❈❊❉✌✳Þ❋✌❈❆★ ✯tØ❘✠➎✓✪➴➌➴ ➘ ✁✬Ô⑤✕ ✠ ➘ ✢✭✠➋✠ ➘ ☛P✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌➈✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮➒✄✝✁✒✩✡☛✖✣✚✷ ➘ ✢✖✫✒✓✪✕✡➮➡✩✡☛✍✆✗✠ ➘ ✻☎✹✝✑✍✢✛✕Ö✑✍✢✛✣✪✑✍✞✗✣✪✢✭✠☞☛★✢ ✑✍✣✪✢✛➴❀➴✚✁✛✥❅✥❪✁✛✌✜✄❉✞✗✣✪✢❛✓✪✕➒✠ ➘ ☛➞✑✘✁☎✕❭❬❀✞✗✕✗✑✘✠❀✓✔✫✛☛➌✕✡✁✛✌✜✄➈✢✛✣➂✥❪✁✛✌✜✄ ✷❴✣✪❪✓ ✴✛☛➋✥❪✁✛✌✜✄❉✞✗✣✪✢➡✷❷Ð✬✹☞✹✚✓✪✕ ✆✟✢✭✌✜✢✛✣✪✣✔☛✖✣①➷⑥✑✘✁☎✕✗➴☞☛✖✑✍✞✡✠❀✓✔✫✛☛✏✄✝✁✒✩✡☛❺✷❴✓✪✕➈✠⑥Ô✂✁✝➴☞✠☞☛✍✆✟➴❨✹✜✯ ✫ ☛❽✑✘✁☎✕✗➴❀✓✪✩✡☛✍✌❻✠ ➘ ✢✭✠✂✠ ➘ ☛❽✑✘☛✖✣✪✣✪✞✗✣✪✢✭✌ ✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮➋➴ ✃ ➴☞✠☞☛✖✄ ✓✪➴⑤✢✭❐✟✣✔☛❂✠☞✁➌➴☞✁☎✣✔✫✛☛❹❲✧➷⑥✑✘✁☎✄✝✆✟✣✔☛✍✠☞☛✚✆✗✌❀✁✛❐✟✣✔☛✖✄➈➴❜✓✪✕➎✆✤✁☎✣ ✃ ✕✡✁☎✄➈✓✪✢✛✣ ✠❀✓✪✄✝☛✝✩✗✞✡☛❺✠☞✁ ➘ ✓✔➮ ➘ ✩✡☛✍➮✛✌❀☛✍☛✝✁✛✥✂✑✘✁☎✄✝✆✟✞✡✠❀✢✭✠❀✓✔✁☎✕ ✆✟✢✭✌✜✢✛✣✪✣✔☛✖✣✪✓✪➴❀✄❙✷❪✥❪✁✛✌✚✓✪✕✗➴☞✠❀✢✛✕✗✑✘☛✛✮✴✠ ➘ ☛ Ô✂☛✖✣✪✣①➷✵✒✴ ✕✡✁✬Ô⑤✕✤æ◆é✙ê❖❋❅✳ ✆✗✌❀✁✛❐✟✣✔☛✖✄➌✹✜✯ ✯✲✱✌✳Ó✷❴✓✰✯ ☛✛✯ ❒✵✕✗✓✔✠☞☛➒✢✛✞✡✠☞✁☎✄➈✢✭✠☞✁☎✕✵✹➞❐✤☛✖✓✪✕✡➮✾✢✛✕ ✢✛✕✗✢✛✣✔✁✛➮✛✁☎✞✗➴❛✁✛✥❺✠☞✌✜✢✛✕✗➴❀✓✪➴☞✠☞✁✛✌✜➴ ✑✍✢✛✕ ❐✤☛❉✁✛✥❻➴☞☛✍✫✛☛✍✌✜✢✛✣♥✠ ✃ ✆✤☛✖➴❽✓✪✕P✩✡☛✍✆✤☛✖✕✗✩✡☛✖✕✗✑✘☛❉✁✛✥➂➮✛☛✖✕✡☛✍✠❀✓✪✑❺✑✘✁☎✕✗➴☞✠☞✌✜✞✗✑✘✠❀✓✔✁☎✕P✁✛✥❻✑✘☛✖✣✪✣✪➴✍✯ ✘ ➴❀✓✪✄✝✆✟✣✔☛✖➴☞✠❉✠ ✃ ✆✤☛✖➴✝✁✛❣ ✥ ✯✲✱✌✳ ✄➈✢ ✃ ❐✤☛➞✌❀☛✍✆✗✌❀☛✖➴☞☛✖✕✺✠☞☛✖✩⑧✢✛➴➋✢➥✩✡☛✍✠☞☛✍✌✜✄➈✓✪✕✗✓✪➴☞✠❀✓✪✑➈❒✗➷ ✕✗✓✔✠☞☛✏✢✛✞✡✠☞✁☎✄➈✢✭✠❀✢❉Ô⑤✓✔✠ ➘ ✶✚✢✛✞✡✠☞✁☎✄➈✢✭✠☞✁☎✕➞➴☞✠❀✢✭✠☞☛✖➴ ➘ ✢✖✫✒✓✪✕✡➮❉✢✛✣✔✆ ➘ ✢✭❐✤☛✍✠❀➴➂✁✛▲✥ ✚ ❨ ➴ ✃ ✄✚❐✤✁☎✣✪➴✍✯ ä➂✢✭✌✜✓✪✢✭❐✟✣✔☛✖✽ ➴ ➧➨✾❚➩❼➫➞✢✛✕✗➍ ✩ ➭❼➲❵❙✎➳❭➫➞✑✘✁✛✌❀✌❀☛✖➴☞✆✤✁☎✕✗✩ ✠☞✁➥✢✛✑✘✠❀✓✔✫✛☛★✢✛✕✗✩↕✓✪✕✗✢✛✑✘✠❀✓✔✫✛☛➎➴☞✠❀✢✭✠☞☛✖➴✝✁✛✥ ➮✛☛✖✕✡☛✛✮➝✌❀☛✖➴☞✆✤☛✖✑✘✠❀✓✔✫✛☛✖✣ ✃ ✯ ➹❅➘ ☛✍✌❀☛❺✢✭✌❀☛✝✩✗❁✓ ▼✤☛✍✌❀☛✖✕✺✠✏✠ ✃ ✆✤☛✖➴✏✁✛✥❄✯✲✱✌➯ ✳ ❐✤✁✛✠ ➘ Ô⑤✓✔✠ ➘ ✆✤✁☎➴❀✓①➷ ✠❀✓✔✫✛☛✝✢✛✕✗✩ ✕✡☛✍➮☎✢✭✠❀✓✔✫✛☛❺✠ ✃ ✆✤☛❺✁✛✥➂➮✛☛✖✕✡☛❺✠☞✌✜✢✛✕✗➴❀✑✘✌✜✓✔✆✗✠❀✓✔✁☎✕★✌❀☛✍➮☎✞✗✣✪✢✭✠❀✓✔✁☎✕★✆✗✌❀✁✒✑✘☛✖➴❀➴✍✯ ➹❅➘ ☛ ✃ ✑✍✢✛✕➞✥❴✞✗✣①❒✵✣✪✣✗✣✔✁✛➮☎✓✪✑✍✢✛✣✟✥❴✞✗✕✗✑✘✠❀✓✔✁☎✕✗❇ ➴ ❉③①❺✮♠ë❊❉③①❺✮♠❈❊❉✌✳ì❋✌❈❆★ ⑧ ✮ ❋✌❈❆Ù Ï ✶✛❁Ñ ✭✤Ï ❂✬Ñ➀✮➝Ï①Ð✖✶❬Ñ➀✯ ➹❅➘ ☛✍✁✛✌❀☛✍✠❀✓✪✑✍✢✛✣✪✣ ✃ ✮✳✓✔✠❻✓✪➴✧✆✤✁☎➴❀➴❀✓✔❐✟✣✔☛◆✠☞✁✚✥❪✁✛✌✜✄ ✢❂❐✟✓✔✁☎➴ ✃ ➴☞✠☞☛✖✄t✁✛✥✴✣✪✓✔✫✒✓✪✕✡➮❂✑✘☛✖✣✪✣✪➴✏✷❪✥❴✞✗✣①❒✵✣✪✣✪✓✪✕✡➮ ✻✖❝❭✶ ✗ ✓✔✁✒✑✘✁☎✄✝✆✟✞✡✠❀✓✪✕✡➮✝➴ ✃ ➴☞✠☞☛✖✄ ✁✛✥♥✣✪✓✔✫✒✓✪✕✡➮❺✑✘☛✖✣✪✣✪➴ ✣✔✁✛➮☎✓✪✑✍✢✛✣✴✥❴✞✗✕✗✑✘✠❀✓✔✁☎✕✗➴❨✹❻✠ ➘ ✢✭✠⑤✑✘✁✛✌❀✌❀☛✖➴☞✆✤✁☎✕✗✩➞✠☞✁➋✢✛✕ ✃ ✣✔✁✛➮☎✓✪✑✍✢✛✣➝➴❀✑ ➘ ☛✖✄✝☛✛✯ í q❃Ù☎q ➼ q ❺ ➺ ➪ q❃t Ï①Ð❨Ñ❹❲➂✌✜✓✔➮✛✁✛➮☎✓✪✕✝Ø❨✯♠î✦ïðÐ✁Ð✂ï ñ⑧❰✖➱✰ï✝ò✖❒ró✪➱✰✃✂❐➪ô☎➱✰❐♠✃✠❒✂Ð③❰❚õ✪ö✦÷❅ï✎ø❚Ï❪ø✠ù✖ï✎ô✁❰❚Ï✺ú❀✃➊öû❒✼✃✢ü❵✘✏✩✡✫✵✯ ✗ ✔✓ ✁☎✣✰✯ ✦★☛✖✩✴✯★❲ ➘✺✃ ➴✍✯➝☎Ð ➾❵✜✏Ð☎❝➦❂✖✺❂ ✮✟✆✗✆➝✯ ❝✖❝☎✵✭ Ð✛Ð✖✶✳✯ Ï ✻✬❹ Ñ ❤✏✢❚✴✛☛✖➞ ✕ ❤✚✯❛✎ ✃ ✕✡☛✍✌❀➮✛☛✍✠❀✓✪✑✍➴✍✯②ý✌õ✉þ✁õ★➱✰✃➊ø☎ö❚❐➪ô☎➱✰ï✎ø❚õ ÿ⑨ø❚õ❼❒ ✁ ❐♠ï✝Ï ï✄✼ ✂ ✃✂ï✝❐✆☎✞✝✠✟♠❰❭Ð☎❒ ✌ ❰✖➱✰ï✎ø❚õ➔ï✝✎ õ ✝✠✟✑✏❭Ð✂ï✎ô✼✓Ð ✒✕✔✖⑧ ✟ ❒✗☎✽ïðÐ✼➱✰✃✘✏➶❰❚õ✪ö ✡ ✃➊❰❚õ⑧Ð✂ï✰➱✰ï✎ø❚õ⑧Ð❶❰❚õ✪ö➍ó✸❒✼Ï ❮☞☛❊ú❀✃✎ùû❰❚õ➪✍ï ☎ ÷❅ï✎ø❚Ï❪ø✠✙ ù ✏➦ü ➃✭❜ä ✤❤ ✽❢ ✛✚ ✠✴ ☎❝➦❂❚✕ ✗ ➝✎✳✆✗✌✜✓✪✕✡➮✛☛✍✌ ✧☛✍✌✜✣✪✢✭➮ ☛✍✌✜✣✪✓✪✕ ⑤☛✖✓✪✩✡☛✖✣✔❐✤☛✍✌❀➮ ⑤☛✍Ô ➂✁✛✌ ✵✮✪Ð ✳✯ Ï ✶✬Ñ❺✙☎✢✛✑✘✁✛❐ ✜ ø❚ÏÕ❒✠ô✢❐♠Ï❪❰❚✃ ÷❅ï✎ø❚Ï❪ø✠✙ ù ✏➦✢ ü ✝❀✃➊ø✑✼ ✂ ÏÕ❒✗☎❹ÐÝ❰❚õ✪ö Ò ✯ ✛✢ ✕✗✩ ✦★✁☎✕✡✁✒✩ ✙✡✯✛❸ ✝❀✃➊ø❭Ð✵ñ➪❒✠ô☎➱✝Ð✢✴ ü ✦★✁☎➴❀✑✘✁✬Ô✦✜❄❢✏✢✛✞⑧✴✭✢✒✮❚Ð☎❝✖➾❭✶✡✮✟✆✗✆➝✯✪✼ Ð ✶❭✒✭ ✶✖❝✳✯ Ï ✶✭Ñ✤✣❂✁✬✫✭✢✭✌✜➊➴ ✴✒✓✪✓➃❉ ä ✯ ✘✚✯♥✢✛✕✗❶ ✩ ❲➂✌❀✁✭❒✟✽ ✌ ✘✚✯ ä❉✯✦❅ ✥ ❒✠ô✁ø✧☎★✼ ✂ ï✝õ✪❰✖➱✰ï✎ø❚õ✛✼ ✂ ïðÐ✼➱✵✑ ❰ ✼ ✂ ï✝Ï ï✰➱✩✏❸ø❚õ➄✪➱ ✟⑧❒ ✂✠❰❭Ð✂ïðÐrø☛❮❀Ð✂ï❪✙ ù ☎❘ø❚ï✎ö✬✫❭ï✝õ❼❒✢➱✰ï✎ô✼Ð❅ø☛❮❇✃✠❒✵ù✖❐♠Ï❪❰✖➱✵ø❚✃✘✏❱❒✼õ✆✌✗✏✧■ ☎ ❒✂Ð✢ü ✗ ✓✔✁✭❒✟➱✖❪✓ ✴✭✢✒✮✺✶✛✶✳✮✟Ð☎❝✖✕✖✳ ✕ ✮ ✆✗✆➝✪✯ ❂❚❨✖✕☎✭⑧❂❚✛➾ ✻P✷❴✓✪✕②⑤ ❍ ✞✗➴❀➴❀✓✪✢✛✕✵✹✜✯ Ï ❨✬✤ Ñ ✣❂✁✬✫✭✢✭✌✜➊➴ ✴✒✓✪✓⑧ä❉✯ ✘✚✯✳✢✛✕✗■ ✩ ➂❲ ✌❀✁✭❒✟✌➃✚ ✘ ✯ ä❉✯ ☎ ❒✠ô✗✟♠❰❚õ➪ïð✘ Ð ☎✉ø☛❮✌➱✔❒✗☎rñ➪❒✼✃➊❰✖➱✰❐♠✃✠❒ ✡ ✃✂ï❪ù➜ù❵❒✼✃✭■ Ð✘✮✺ï✰➱✵ô✗✟ûï✝õ❵ù②ø☛❮③ó★✃➊ô❱ø❚õ✪ô✁ø✠ù❵❒✼õ❼❒✽➱✝Ð✘☛✯☎✽❐⑧➱✵❰❚õ★➱❄ï✝✱ õ ✰r❒✠ø❚✃✎ù✖ï✵❒✼✲ ò ❘ ☎ ø☎öû❒✼Ï❪ü ✗ Ð☎❝✖✕✖✳❝ ✮ ✶❭✶⑧✜◆✆✗✆➝✯✟✻✖❨✖❝☎✒✭ ✻✖➾✛✻P✷❴✓✪✕✤❍⑤✞✗➴❀➴❀✓✪✢✛✕✵✹✜✯ ✓✔✁✭❒✟➱✖❪✓ ✴✭✢✒✮ Ï ➾✬✤ Ñ ✣❂✁✬✫✭✢✭✌✜➊➴ ✴✒✓✪✓▲❉ ä ✯ ✘✚✯✴✢✛✕✗✩❆❲➂✌❀✁✭❒✟✌❣✘✚✯ ä❉✯ ✡ ✃✂ï❪ù➜ù❵❒✼✃❘❒✩✳❣❒✠ô☎➱❅ø☛❮✦✴ ✷ ☛Õ✵ ñ ♠ ✟ ❰☎ù❵❒✦ù❵❒✼õ✪ø✧☎■❒ Ð✘✮✺ï✰➱✵ô✗✟ûï✝õ❵ùûü✵✦★✁☎✣✰✯ ✗ ✓✔✁☎✣✰✯✔✮✡✫✛✁☎✣✰✯✵✖ ✻ ❨✳✮❚Ð☎❝✖✒❝ Ð✭✮✵✆✗✆➝✯✪Ð✖✖✻ ❝✛✶☎✵✭ Ð✖✶✭✸✛✸ ✷❴✓✪✕②⑤ ❍ ✞✗➴❀➴❀✓✪✢✛✕✵✹ Ï ❂✖✤ Ñ ✣❂✁✬✫✭✢✭✌✜➊➴ ✴✒✓✪✓✺ä❉✯ ✘✚✯❚✢✛✕✗✩❸➂❲ ✌❀✁✭❒✟✌⑨✚ ✘ ✯ ä❉✯ ✃ ☎❘ø☎öû❒✼Ï❀ø☛❮❜❰❚Ï✝ÏÕ❒✼Ï ï✎ô✽ù❵❒✼õ❼❒◆❒✸✷✙☛ ✡ ✃✂ï❪ù➜ù❵❒✼✶ ➱✰✃➊❰❚õ⑧Ð✢ô✢✃✂ï ñ❼➱✰ï✎ø❚õ➵✃➊❰✖➱✔❒☎❋ ü ✦★✁☎✣✰✯ ✗ ✓✔✁☎✣✰✯✔✮✚✫✛✁☎✣✰✯❋✶✒Ð✭✮ Ð ❝✖✒❝ Ð✭✮ ✗✆ ✆➝✯ ✶➦❂✖❂✢✒✭ ✶✖✕✭✸✒✯ ➹ ✌✜✢✛✕✗➴❀✣✪✢✭✠☞☛✖✩Õ✥❪✌❀✁☎✄ Ð☎❝✖❝➦✺❂ ✯★✦★✁☎✣✔✢☛ ✒✴ ✞✗✣ ✃ ✢✭✌✜✕✗✢ ✃ ✢ ✗ ✓①➷ ☎ ✁☎✣✔✁✛➮☎✓ ✃ ✢✒✟✮ ✫✛✁☎✣✰✯✟✶✒Ð✭✪✮ ❢⑤✁✡✯✵✶✳✮✗✆✗✆➝✯ ✶û❨❭✶❭✭û✶û❨➦❂✺✯✧✷❴✓✪✤ ✕ ⑤ ❍ ✞✗➴❀➴❀✓✪✢✛✕✵✹ ñ✪✃✠❒✂Ð✁Ð✂ï✎ø❚õ✪ü❱î❹✧ ø ☎✽ï✝õ✪❰❚õ✪ô✂❒❶ï✝õ Ï ✕✬✤ Ñ ✣❋✢✭✌✜✓ ➅ ✔✯ ✮✧✣❋✢✭✌✜✓✺✙✡✯✔✮ ➅ ✢✛✕✗✩✡Ô✂☛✍❐✤☛✍✌ ➅ ✯ Ò ✯✧✥❅❒✼ò✖❒✼✃✁Ð✂ï✄✼✂ ÏÕ❒✹☎❘ø❚ÏÕ❒✠ô✢❐♠Ï❪❰❚✃❇ô✁✧ø ☎rñ✪❐⑧➱✵❰✖➱✰ï✎ø❚õ ï✝õ❆ô✢ï✝Ï ï✎❰✖➱✔❒✂Ð✢✒ ü Ø❷✕➞✙✛☛✍Ô✂☛✖✣✪➴◆✢✭✌❀☛ Ò ✁✛✌❀☛✍✫✛☛✍✌✖✺ ✮ ❋ ✣ ✢✭✌ ➘ ✞✗✄➈❚ ✢ ✴✒✓✵✙✡❪✯ ➂✡✦P✢✛✞✡✌❀☛✍✌❀❤✚❪✯ ➂➪✼ ❲ ✢✛ ✻ ✞✗✕ Ó❉✯❪➂★❅ ❍ ✁✛➱✍☛✖✕✺❐✤☛✍✌❀➮◆Ó❉✯✔✮♥✷ ✚ ✩✗➴❨✹✜✯✵✎✳✆✗✌✜✓✪✕✡➮✛☛✍✌☞✵➷ ✧ ä ☛✍✌✜✣✪✢✭➮➎☎ Ð ❝✖❝✖✳❝ ✮✵✆✗✆➝✯ ✶✖❨✛✶☎✒✭ ✶✖➾✛✶✳✯ Ï ❝✬❹ Ñ ✘✏✄✝✁☎➴✧✦➡✯✛✢✛✕✗✩❘✏ ➏ Ô✂☛✖✕✗➴☞✁☎✕❘❉ Ó ✯ Ó❉✯ ✚ ❍❅✂Ø❷✛ ✦ ⑤ ❢ ☛✍Ô⑤➴➋✶✺✶✳✮☎✆✗✆➝✯✛✶✖➾☎✒ ✭ ✶➦✺ ❂ ⑧ ✮ ➏❽✑✘✠☞✁✛❐✤☛✍✌ ✻✭✸✛✸✛✸✒✯ ✻✖❝✖❨ ✏✞✡✌❀☛✖✣✪✓✪❳ ✢ ❲➂✌❀✁✭❒✟✌ ✘ Ï①Ð✍✸❬Ñ✽❲➂✠❀✢✛➴ ➘ ✕✡☛➥✦➡r ✯ ✽ ý r ✰ ❒✼õ❼❒✢➱✰ï✎ô❆ó✵✺ ✮ ï✰➱✵ô✗✟♠ü★r ✰ ❒✼õ❼✾ ❒ ✺ ✔ ø❚õ★➱✰✃➊ø❚Ï⑨❰❚õ✪ö➽✷✴☛③ñ✵♠ ✟ ❰☎ù❵❒✘✒✿✂✗✏ ÷❅Ï❪❰➦✗ ô ✫❀✮❄❒✼Ï✝Ï✸ó❼ô✢ï✵❒✼õ★➱✰ï ❁❄ô❂❀ ✝ ❐✵✼ ✂ Ï ï✎ô✁❰✖➱✰ï✎ø❚õ⑧Ð❹❰❚õ✪❃ ö ✔❃❒✼Ï✝Ï❄✝❀✃✠❒✂Ð✁Ð✓➂ ✒ ☎ Ð ❝✖✕➦✺❂ ✯ Ï①Ð✛Ð❨Ñ✽✘ ➘ ❡ ✁ ✚ ✘ ✯ ä❉✯✔✮✺Ò✏✣✪✣✪✄➈✢✛✕➒✙✡✯ ❞❉✯ ✡ ✟⑧❒ ✡ ✟⑧❒✠ø❚✃✘✏❊ø☛❮❅✝❅❰❚✃✁Ð✂ï✝õ❵✧ ù ✒ ✡ ✃➊❰❚õ⑧Ð✂Ï❪❰✖➱✰ï✎ø❚õ④❰❚õ✪ö ✔✺ø✧☎rñ✪ï✝Ï ï✝õ❵ùûü❼➂ ❲ ✌❀☛✖✕✺✠❀✓✪✑✘☛❽➷❄❤✏✢✛✣✪✣✰✮✡Ø❷✕✗✑✭✯ ✚ ✕✡➮☎✣✔☛✍Ô✂✁✳✁✒✩★◆✣✪✓❁▼✴➴✍⑧ ✮ ❢✚✯✵✙✡✯✔✮➝☎Ð ❝➦✭❂ ✶✳✯ Ï①Ð✖✻✬✽ Ñ ❞❽✢✭✁✭✄➷ ❽ ❆ ✓✪❃ ✞ ❇ ➘ ✁☎✞✴❄✯ ✥❅❒✵ù✖❐♠Ï❪❰✖➱✵ø❚✘✃ ✏❈☎■❒✠ô✗✟♠❰❚õ➪ïð✘Ð ☎Þø☛❮❀ñ✪Ï❪❰❚õ★➱❃ù❵❒✼õ❼❒⑨➱✰✃➊❰❚õ⑧Ð✢ô✢✃✂ï ñ❼➱✰ï✎ø❚õ ✂✗✏✱✰ ✡ ☛✠❒✼ÏÕ✗ ❒ ☎■❒✼õ★➱✝Ð✤❰❚õ✪✱ ö ✰ ✡ ☛ ❮✢❰➦ô☎➱✵ø❚✃✁Ð✢ü ➹ ✌❀☛✖✕✗✩✗➴❉✓✪✕❶❲❻✣✪✢✛✕✺✠✝✎✒✑✍✓✔☛✖✕✗✑✘☛✛✯✧✙☎✞✗✕✡☛✛✮ ✫✛✁☎✣✰➪✯ ✡✶ ★✮ ✚ ❢ ✪ ✯ ➾✳✮✪Ð☎❝✖❝✖✳❝ ✮✵✆✗✆➝✯✗✻✒Ð✍➜✸ ✒✭ ✻✒Ð✼✶✡✯ Ï①Ð✖✶✬✽ Ñ ❲➂✌❀✁✭❒✟✌✖✮Ý✘✚✯ ✡ ✟⑧❒❩✘Ð ✏❭Ð✼➱✔✗❒ ☎ ø☛❮❉❘ ☎ ø❚ÏÕ❒✠ô✢❐♠Ï❪❰❚✃✘☛✎ù❵❒✼õ❼❒✢➱✰ï✎ô ➱✰✃✂ï❪ù➜ù❵❒✼✃✁Ð ❰❭Ð ❰ Ð☎❒✼Ï ❮✘☛➊ø❚✃✎ùû❰❚õ➪✍ï ✼ ✌ ï✝õ❵ù ô✁✧ ø ☎rñ✪❐⑧➱✰ï✝õ❵ù④Ð✘✏❭Ð✼➱✔❒✗☎❘✍ü ☛❊✺ ✔ ✧ ø ☎rñ✪❐⑧➱✔❒✼✃➽ó❼ô✢ï✵❒✼õ✪ô✂❒ ⑧ ❋ ø❚❐♠✃✂õ✪❰❚Ï✽ø☛❮ ❃✻✭✸✛✸✡Ð✭✮✵✕✴✯ ✻✳✮✗✆✗✆➝★✯ ❨❭✭✶ ➷☛❂✳Ð✭✯ Ï①Ð✼✶✭Ñ✽❲➂✌❀✁✭❒✟✌✽✘✚❃✯ ÷❅ï✎ø☎ô✁ø✧☎rñ✪❐⑧➱✰ï✝õ❵ù❊Ð✘✏❭Ð✼➱✔❒✗☎ ✜❸ø❚Ï❪ö➦ø❚ò❚❰❀✒ ø☛❮■Ï ï✝ò➜ï✝õ❵ù❸ô✂❒✼Ï✝Ï Ð✢✹ ü ✝❀✃✠❒✗☛Õñ✪✃➊ø☎ô✂❒✁❒✠ö❚ï✝õ❵ù❚Ð②ø☛❮ ❅✙☎✞✗✕✡☛ î❣ÿ✌ý❂❍■☛❣þ✁õ★➱✔❒✼✃✂õ✪❰✖➱✰ï✎ø❚õ✪❰❚✠ Ï ✜➽❒✁❒✢➱✰ï✝õ❵ù❊ø❚õ❶î❣ÿ✌ý✉÷✌❰❭Ð☎❒✠✾ ö ✺ ✔ ø✧☎rñ✪❐⑧➱✔❒✼✃✁Ð✓✒ Ð✍✸➜✵✭ Ð✖✶✳✮✴✻✭✸✛✸☎✻✳✮➝✎✒✢✭✆✗✆✤✁✛✌❀✁✡✮✗✙☎✢✭✆✟✢✛✕✴✮✡✆➝✯✟✶✛✶✖❨✳✯ ø ✏ ï ❑▼✡▲ ó➀✓ò ❬◆ ó ❏ õ✬ó➀☛ ü✪❱❬ð❴÷➀ï ÷➀õ✬÷➀ø♥ò✓❲ ❏ ö❬ö❭✏ ï ø☞ù✼▲✗î✍û✬ð✰ï ✡❷ð❘❯ ø ◗❻û❅ò✓✵❲ ý☎❷✡ ï ø❘❱❭✡❷ø❷ð❘❯ ❏ ✡❚❑❨ù✬❘ ❖❚ø❷ö❬õ❬❭ ú ✏ ï ✡✧✓ò ★❲ ✏ ✍ ò✂✏ ù✬✸ò P✘❑❳❯ ð❴÷✰ó➊✓ ❏ ✡❚❑❨ù✬❘ø ◗❻✼ û ❨❊❯✖✑✵î❬✍ï ð✰❩ ï ❱❭❑✜❬ ✑õ ❯ ✁ÿ ✘ÿ✁❚✞ ❪➜✼ ✍ ❫✠❯û✏ ✍ ò✂✏ ù✬✸ò P✘❑ ❑ ï ✏❜❛❄❝❳❞✧❡✘❢✸❣ ❤✍❝❀✐❦❥✯❥✓❧ ❝❳❥✯❝❳♠✧❧ ♥✼♠ ❴ ❪❊◗❵✜ ❚ø ❷ø❷ï P✘ø☞ù❽ý✖ø❷ö✬÷➀❘ø ◗✂ú✛ø❘ó❖✄❚❙❀þ✪÷➀✑î ✛❯ ÿ✁✂✘ÿ ❖ ☛✡ ✻✖❝✖➾
Deductive biocomputing. Deductive Biocomputing
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