Add new SentenceTransformer model

3f4b668 verified 9 months ago

84.2 kB

tags:
  - sentence-transformers
  - sentence-similarity
  - feature-extraction
  - generated_from_trainer
  - dataset_size:1124250
  - loss:CoSENTLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget:
  - source_sentence: "with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone's\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n\"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced.\"\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe"
    sentences:
      - >-
        Quantum Statistics 187

        0

        1

        2

        3

        ¯n

        −2 −1 0123

        α+βϵ

        Figure 8.1: A comparison of the Bose-Einstein (solid curve),
        Maxwell-Boltzmann (dashed curve),

        and Fermi-Dirac (dash-dotted curve) distributions.

        Finally, the partition function of the gas is given by

        ln Z =αN ±

        ∑

        r

        ln

        (

        1 ±e−α−βϵr

        )

        . (8.58)

        Let us investigate the magnitude ofαin some important limiting cases.
        Consider, ﬁrst of all,

        the case of a gas at a given temperature when its concentration is made
        suﬃciently low: that is,

        when N is made suﬃciently small. The relation (8.57) can only be
        satisﬁed if each term in the

        sum over states is made suﬃciently small; that is, if ¯nr ≪1o rα+βϵr ≫1
        for all statesr.( S e e

        Figure 8.1.)

        Consider, next, the case of a gas made up of a ﬁxed number of particles
        when its temperature is

        made suﬃciently large. That is, whenβis made suﬃciently small. In the
        sum in Equation (8.57),

        the terms of appreciable magnitude are those for whichα+βϵr <1. (See
        Figure 8.1.) Thus, it

        follows that asβ→0 an increasing number of terms with large values ofϵr
        contribute substantially

        to this sum. In order to prevent the sum from exceedingN, the
        parameterαmust become large

        enough that each term is made suﬃciently small: that is, it is again
        necessary that ¯nr ≪1o r

        α+βϵr ≫1 for all statesr.

        The previous discussion suggests that if theconcentration of an ideal
        gas is made suﬃciently

        low, or the temperature is made suﬃciently high, thenαmust become so
        large that

        exp(α+βϵr) ≫1 (8.59)

        for allr. Equivalently, this means that the number of particles
        occupying each quantum state must

        become so small that

        ¯nr ≪1 (8.60)
      - "myriads\tas\tto\tstain\tthe\tberg\tand\tthe\tpack\tice\twherever\tthey\twere\twashed\tby\tthe\nswell\tof\tthe\tsea;\tand,\twhen\tenclosed\tin\tthe\tcongealing\tsurface\tof\tthe\twater,\tthey\nimparted\tto\tthe\tbrash\tand\tpancake\tice\ta\tpale\tochreous\tcolour.\tIn\tthe\topen\tocean,\nnorthward\tof\tthe\tfrozen\tzone,\tthis\torder,\tthough\tno\tdoubt\talmost\tuniversally\npresent,\tgenerally\teludes\tthe\tsearch\tof\tthe\tnaturalist;\texcept\twhen\tits\tspecies\tare\ncongregated\tamongst\tthat\tmucous\tscum\twhich\tis\tsometimes\tseen\tfloating\ton\tthe\nwaves,\tand\tof\twhose\treal\tnature\twe\tare\tignorant;\tor\twhen\tthe\tcoloured\tcontents\nof\tthe\tmarine\tanimals\twho\tfeed\ton\tthese\tAlgae\tare\texamined.\tTo\tthe\tsouth,\nhowever,\tof\tthe\tbelt\tof\tice\twhich\tencircles\tthe\tglobe,\tbetween\tthe\tparallels\tof\n50°\tand\t70°\tS.,\tand\tin\tthe\twaters\tcomprised\tbetween\tthat\tbelt\tand\tthe\thighest\nlatitude\tever\tattained\tby\tman,\tthis\tvegetation\tis\tvery\tconspicuous,\tfrom\tthe\ncontrast\tbetween\tits\tcolour\tand\tthe\twhite\tsnow\tand\tice\tin\twhich\tit\tis\timbedded.\nInsomuch,\tthat\tin\tthe\teightieth\tdegree,\tall\tthe\tsurface\tice\tcarried\talong\tby\tthe\ncurrents,\tthe\tsides\tof\tevery\tberg\tand\tthe\tbase\tof\tthe\tgreat\tVictoria\tBarrier\titself,\nwithin\treach\tof\tthe\tswell,\twere\ttinged\tbrown,\tas\tif\tthe\tpolar\twaters\twere\tcharged\nwith\toxide\tof\tiron.\n\"As\tthe\tmajority\tof\tthese\tplants\tconsist\tof\tvery\tsimple\tvegetable\tcells,\tenclosed\nin\tindestructible\tsilex\t(as\tother\tAlgae\tare\tin\tcarbonate\tof\tlime),\tit\tis\tobvious\tthat\nthe\tdeath\tand\tdecomposition\tof\tsuch\tmultitudes\tmust\tform\tsedimentary\tdeposits,\nproportionate\tin\ttheir\textent\tto\tthe\tlength\tand\texposure\tof\tthe\tcoast\tagainst\nwhich\tthey\tare\twashed,\tin\tthickness\tto\tthe\tpower\tof\tsuch\tagents\tas\tthe\twinds,\ncurrents,\tand\tsea,\twhich\tsweep\tthem\tmore\tenergetically\tto\tcertain\tpositions,\tand\nin\tpurity,\tto\tthe\tdepth\tof\tthe\twater\tand\tnature\tof\tthe\tbottom.\tHence\twe\tdetected\ntheir\tremains\talong\tevery\ticebound\tshore,\tin\tthe\tdepths\tof\tthe\tadjacent\tocean,\nbetween\t80\tand\t400\tfathoms.\tOff\tVictoria\tBarrier\t(a\tperpendicular\twall\tof\tice\nbetween\tone\tand\ttwo\thundred\tfeet\tabove\tthe\tlevel\tof\tthe\tsea)\tthe\tbottom\tof\tthe\nocean\twas\tcovered\twith\ta\tstratum\tof\tpure\twhite\tor\tgreen\tmud,\tcomposed\nprincipally\tof\tthe\tsilicious\tshells\tof\tthe\t\nDiatomaceoe\n.\tThese,\ton\tbeing\tput\tinto\nwater,\trendered\tit\tcloudy\tlike\tmilk,\tand\ttook\tmany\thours\tto\tsubside.\tIn\tthe\tvery\ndeep\twater\toff\tVictoria\tand\tGraham's\tLand,\tthis\tmud\twas\tparticularly\tpure\tand\nfine;\tbut\ttowards\tthe\tshallow\tshores\tthere\texisted\ta\tgreater\tor\tless\tadmixture\tof\ndisintegrated\trock\tand\tsand;\tso\tthat\tthe\torganic\tcompounds\tof\tthe\tbottom\nfrequently\tbore\tbut\ta\tsmall\tproportion\tto\tthe\tinorganic.\"\t…\n\"The\tuniversal\texistence\tof\tsuch\tan\tinvisible\tvegetation\tas\tthat\tof\tthe\tAntarctic\nOcean,\tis\ta\ttruly\twonderful\tfact,\tand\tthe\tmore\tfrom\tits\tnot\tbeing\taccompanied\nby\tplants\tof\ta\thigh\torder.\tDuring\tthe\tyears\twe\tspent\tthere,\tI\thad\tbeen\naccustomed\tto\tregard\tthe\tphenomena\tof\tlife\tas\tdiffering\ttotally\tfrom\twhat"
      - >-
        The ‘Computational Unified Field Theory’ (CUFT):  

        Harmonizing Quantum and Relativistic Models and Beyond 
         
        537 

        Tg : ∑oi{x,y,z}[USCF(n)] ≠ oj{(x+m),(y+m),(z+m)} [USCF(1...n)] /c x
        n{USCF’s}, 

        such that:  

        T: ∑oi{x,y,z}[USCF(n)] - oj{(x+m),(y+m),(z+m)} [USCF(1...n)] ≤ c x
        n{USCF’s}  

        The temporal value of an event (or object) is computed based on the
        number of times that a 

        given object or event has changed – relative to the speed of light
        (e.g., across a certain 

        number of USCF's); However, the measurement of temporal changes (e.g.,
        taking place at an 

        object or event) differ significantly – when computed from the 'global'
        or 'local' perspectives: 

        This is because from a 'global' perspective, the faster an object
        travels (e.g., relative to the 

        speed of light) the less potential changes ar e exhibited in that
        object's or event's 

        presentations (across the relevant series of USCF 's). In contrast, from
        a 'local' perspective, 

        there is no change in the number of measured changes in the given object
        (e.g., as its 

        velocity increases relative to the speed of light) – since the local
        (computational) perspective 

        does not encompass globally measured changes in the object's
        displacement (relative to the 

        speed of light)…  

        Note also that we can begin appreciating the fact that from the CUFT’s
        (D2 USCF’s) 

        computational perspective there seems to be inexorable (computational)
        interrelationships 

        that exist between the eight computational prod ucts of the three
        postulated Computational 

        Dimensions of ‘Framework’, ‘Consistency’ and ‘Locus’; Thus, for
        instance, we find that an 

        acceleration in an object’s velocity increases the number of times that
        object is presented 

        (e.g., 'globally' across a given number of USCF  frames) – which in tu
        rn also increases it 

        ‘mass’ (e.g., from the ‘global Locus’ computational perspective), and
        (inevitably) also 

        decreases its (global) ‘temporal’ value (due to  the decreased number of
        instances that that 

        object changes across those given number of fram es (e.g., globally-
        relative to the speed of 

        light maximal change computational constraint)... Indeed, over and
        beyond the 

        hypothesized capacity of the CUFT to replicate and account for all known
        relativistic and 

        quantum empirical findings, its conceptually  higher-ordered ‘D2’ USCF’s
        emerging 

        computational framework may point at the unification of all apparently
        “distinct” physical 

        features of ‘space’, ‘time’, ‘energy’ and ‘mass’ (and ‘causality’) as
        well as a complete 

        harmonization between the (apparently disparat e) quantum (microscopic)
        and relativistic 

        (macroscopic) phenomena and laws; the apparent disparity between quantum
        (microscopic) 

        and relativistic (macroscopic) phenomena and laws; 

        Towards that end, we next consider the a pplicability of the CUFT to
        known quantum 

        empirical findings: Specifically, we cons ider the CUFT’s account of the
        quantum 

        (computational) complimentary properties of ‘space’ and ‘energy’ or
        ‘time’ and ‘mass’; of an 

        alternative CUFT’s account of the “collapse” of the probability wave
        function; and of the 

        ‘quantum entanglement’ and ‘p article-wave duality’ subatomic phenomena;
        It is also 

        hypothesized that these alternative CUFT’s th eoretical accounts may
        also pave the way for 

        the (long-sought for) unification of quantum and relativistic models of
        physical reality. First, 

        it is suggested that the quantum complimentary ‘physical’ features of
        ‘space’ and ‘energy’, 

        ‘time’ and ‘mass’ – may be due to a ‘computational exhaustiveness’ (or
        ‘complimentarity’) of 

        each of the (two) levels of the Computational Dimension of ‘Framework’.
        It is hypothesized 

        that both the ‘ frame’ and ‘object’ (‘D2-USCF’s’) computational
        perspectives are exhaustively 

        comprised of their ‘consistent’ (e.g., ‘space’ and ‘energy’, or ‘mass’
        and ‘time’ physical 

        features, respectively): Thus, whether we chos e to examine the USCF’s
        (D2) computation of
  - source_sentence: "with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone's\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n\"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced.\"\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe"
    sentences:
      - "multiplication\tresults\tin\tthe\tthrowing\toff\tof\tcells,\tinstead\tof\tresulting\tin\tthe\nformation\tof\tmore\ttissue.\tHence,\ttaking\tan\taverage\tview,\twe\tsee\twhy\tthe\tsmaller\nanimals\tso\tsoon\tarrive\tat\ta\treproductive\tage,\tand\tproduce\tlarge\tand\tfrequent\nbroods;\tand\twhy,\tconversely,\tincreased\tsize\tis\taccompanied\tby\tretarded\tand\ndiminished\tfertility.\nBut,\tas\tabove\timplied,\tit\tis\tnot\tso\tmuch\tto\tthe\tbulk\tof\tthe\tbody\tas\ta\twhole,\tas\tto\nthe\tbulk\tof\tthe\tnervous\tsystem,\tthat\tfertility\tstands\trelated\tamongst\tthe\thigher\nanimals.\tProbably,\tindeed,\tit\tstands\tthus\trelated\tin\tall\tcases;\tthe\tdifference\nsimply\tarising\tfrom\tthe\tfact,\tthat\twhereas\tin\tthe\tlower\torganisms,\twhere\tthe\nnervous\tsystem\tis\tnot\tconcentrated,\tits\tbulk\tvaries\tas\tthe\tbulk\tof\tthe\tbody,\tin\tthe\nhigher\torganisms\tit\tdoes\tnot\tdo\tso.\tBe\tthis\tas\tit\tmay,\thowever,\twe\tsee\tclearly\nthat,\tamongst\tthe\tvertebrata,\tthe\tbodily\tdevelopment\tis\tnot\tthe\tdetermining\ncircumstance.\tIn\ta\tfish,\ta\treptile,\ta\tbird,\tand\ta\tmammal\tof\tthe\tsame\tweight,\tthere\nis\tnothing\tlike\tequality\tof\tfecundity.\tCattle\tand\thorses,\tarriving\tas\tthey\tdo\tso\nsoon\tat\ta\treproductive\tage,\tare\tmuch\tmore\tprolific\tthan\tthe\thuman\trace,\tat\tthe\nsame\ttime\tthat\tthey\tare\tmuch\tlarger.\tAnd\twhilst,\tagain,\tthe\tdifference\tin\tsize\nbetween\tthe\telephant\tand\tman\tis\tfar\tgreater,\ttheir\trespective\tpowers\tof\nmultiplication\tare\tless\tunlike.\tLooking\tin\tthese\tcases\tat\tthe\tnervous\tsystems,\nhowever,\twe\tfind\tno\tsuch\tdiscrepancy.\tOn\tlearning\tthat\tthe\taverage\tratio\tof\tthe\nbrain\tto\tthe\tbody\tis—in\tfishes,\t1\tto\t5668;\tin\treptiles,\t1\tto\t1321;\tin\tbirds,\t1\tto\n212;\tand\tin\tmammals,\t1\tto\t186;\n[99]\n\ttheir\tdifferent\tdegrees\tof\tfecundity\tare\naccounted\tfor.\tThough\tan\tox\twill\toutweigh\thalf-a-dozen\tmen,\tyet\tits\tbrain\tand\nspinal\tcord\tare\tfar\tless\tthan\tthose\tof\tone\tman;\tand\tthough\tin\tbodily\tdevelopment\nthe\telephant\tso\timmensely\texceeds\tthe\thuman\tbeing,\tyet\tthe\telephant's\tcerebro-\nspinal\tsystem\tis\tonly\tthrice\tthe\tsize\tattained\tby\tthat\tof\tcivilized\t\nmen.\n[100]\nUnfortunately,\tit\tis\timpossible\tto\ttrace\tthroughout\tthe\tanimal\tkingdom\tthis\ninverse\trelationship\tbetween\tthe\tnervous\tand\treproductive\tsystems\twith\tany\naccuracy.\tPartly\tfrom\tthe\tfact\tthat,\tin\teach\tcase,\tthe\tdegree\tof\tfertility\tdepends\non\tthree\tvariable\telements—the\tage\tat\twhich\treproduction\tbegins,\tthe\tnumber\nproduced\tat\ta\tbirth,\tand\tthe\tfrequency\tof\tthe\tbirths;\tpartly\tfrom\tthe\tfact\tthat,\tin\nrespect\tto\tmost\tanimals,\tthese\tdata\tare\tnot\tsatisfactorily\tattainable,\tand\tthat,\nwhen\tthey\tare\tattainable,\tthey\tare\tvitiated\tby\tthe\tinfluence\tof\tdomesticity;\tand\npartly\tfrom\tthe\tfact\tthat\tno\tprecise\tmeasurement\tof\tthe\trespective\tnervous\nsystems\thas\tbeen\tmade,\twe\tare\tunable\tto\tdraw\tany\tbut\tgeneral\tand\tsomewhat\nvague\tcomparisons.\tThese,\thowever,\tas\tfar\tas\tthey\tgo,\tare\tin\tour\tfavour.\nAscending\tfrom\tbeings\tof\tthe\tacrite\tnerveless\ttype,\twhich\tare\tthe\tmost\tprolific\nof\t all,\t through\t the\t various\t invertebrate\t sub-kingdoms,\t amongst\t which"
      - >-
        200 Chapter 7 Superposition of Quasi-Parallel Plane Waves

        COMMENT: As the wave travels, the earlier part of the pulse oscillates

        more slowly than the later part. This is called chirp, and it means

        that the red frequencies get ahead of the blue ones since they experi-

        ence a lower index. The instantaneous frequency is the effective local

        frequency.

        Exercises for 7.6 Generalized Context for Group Delay

        P7.9 When the spectrum of a pulse is narrow compared to the resonant

        spectral features of a material (like that depicted in Fig. 7.10), the
        re-

        shaping delay (7.53) can be neglected. Show that the net delay in this

        case (7.52) reduces to

        lim

        T →∞

        ∆tG (r) = ∂Rek

        ∂ω ·∆r

        ¯¯¯

        ¯

        ¯ω

        HINT: The spectral intensity may be approximated asI (ω) = I0δ(ω− ¯ω).

        P7.10 When the spectrum a pulse is very broad, the reshaping delay
        (7.53) is

        negligible. Show that in this case the net delay reduces to

        lim

        T →0

        ∆tG (r) = ∆r

        c

        assuming k and ∆r are parallel. This implies that a sharply defined

        signal cannot travel faster than c.

        HINT: The real index of refractionn goes to unity far from resonance,

        and the imaginary part κ goes to zero.

        P7.11 Show that equation (7.49) can be written as

        〈t〉 = −i

        ∞R

        −∞

        dω

        h

        ∂

        ∂ωE (r,ω)

        i

        ·E∗ (r,ω)

        ∞R

        −∞

        dωE (r,ω) ·E∗ (r,ω)

        ≡ T [E (r,ω)]

        HINT: Parseval’ s theorem(7.21) can be used in the denominator. In

        the numerator, substitute (7.18) for both fields, with ω and ω′ as the

        dummy variables. Reorder integration to perform the time integral

        first. The following trick is handy:

        1

        2π

        ∞R

        −∞

        t e−i (ω′−ω)t d t = −i ∂

        ∂ω

        1

        2π

        ∞R

        −∞

        e−i (ω′−ω)t d t = −i ∂

        ∂ωδ

        ¡

        ω′ −ω

        ¢

        .

        P7.12 Use the result of P 7.11 to derive (7.51).

        HINT: Compute

        ∆t = T [E (r0 +∆r,ω)] −T [E (r0,ω)].
      - >-
        any element of this algebra can be written as a sum of elements in
        normal order,

        of the form

        cl,m(a†

        B)lam

        B

        with all annihilation operators aB on the right, for some complex
        constantscl,m.

        As a vector space over C, Weyl(2, C) is infinite dimensional, with a
        basis

        1, aB, a†

        B, a2

        B, a†

        BaB, (a†

        B)2, a3

        B, a†

        Ba2

        B, (a†

        B)2aB, (a†

        B)3, . . .

        This algebra is isomorphic to a more familiar one. Setting

        a†

        B = z, a B = d

        dz

        one sees that Weyl(2, C) can be identified with the algebra of
        polynomial coef-

        ficient differential operators on functions of a complex variable z. As
        a complex

        vector space, the algebra is infinite dimensional, with a basis of
        elements

        zl dm

        dzm

        In our study of quantization by the Bargmann-Fock method, we saw that

        the subset of such operators consisting of complex linear combinations
        of

        1, z, d

        dz , z 2, d2

        dz2 , z d

        dz

        is closed under commutators, and is a representation of a Lie algebra of
        complex

        dimension 6. This Lie algebra includes as subalgebras the Heisenberg Lie
        algebra

        h3 ⊗ C (first three elements) and the Lie algebra sl(2, C) = sl(2, R) ⊗
        C (last

        three elements). Note that here we are allowing complex linear
        combinations,

        so we are getting the complexification of the real six dimensional Lie
        algebra

        that appeared in our study of quantization.

        Since the aB and a†

        B are defined in terms of P and Q, one could of course

        also define the Weyl algebra as the one generated by 1, P, Q, with the
        Heisenberg

        commutation relations, taking complex linear combinations of all
        products of

        these operators.

        28.1.2 One degree of freedom, fermionic case

        Changing commutators to anticommutators, one gets a different algebra,
        the

        Clifford algebra:

        Definition (Complex Clifford algebra, one degree of freedom) . The
        complex

        Clifford algebra in the one degree of freedom case is the algebra
        Cliff(2, C) gen-

        erated by the elements 1, aF , a†

        F , subject to the canonical anticommutation rela-

        tions (CAR)

        [aF , a†

        F ]+ = 1, [aF , aF ]+ = [a†

        F, a†

        F]+ = 0

        312
  - source_sentence: "with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone's\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n\"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced.\"\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe"
    sentences:
      - >-
        CHAPTER 

        Moray Offshore Renewables Limited – Environmental Statement  

        Telford, Stevenson and MacColl Offshore Wind Farms and Transmission
        Infrastructure 
         
        Section 3 – Offshore Generating Station Impact Assessment 7-23 

        7.1 

        Decommissioning 

        7.1.6.45 Effects of deco mmissioning activities will be comparable to
        those arising durin g the 

        construction of the wind farms or where cables and other structures
        beneath the 

        surface of the seabed are left in –situ, then effects will be much less
        .  Removal of 

        turbine foundations and scour material will disturb seabed sediments for
        subsequent 

        re–distribution over adjacent areas resulting in potential smothering
        effects as 

        assessed above.  The dominant sediment habitats and co mmunities will be
        tolerant 

        to these effects (as assessed) and the significance of related effects
        is expected to 

        remain minor. 

        7.1.6.46 Removal of the turbines will result in the removal of the
        epifaunal co mmunities 

        attached to them .  A reduction in epibenthos to pre –construction
        conditions is 

        therefore predicted .  Exposed seabed areas are expected to be rapidly 

        re-colonised with full restitution of the habitats and biotopes expected
        within five 

        years, subject to the condition of the seabed substrate and stability
        compa red to 

        the baseline situation. 

        7.1.6.47 Removal of turbines upon which sensitive and  / or protected
        species, such as the 

        cold water coral Lophelia pertusa , have become attached would
        constitute a 

        negative effect .  Current precedent for assessment in this regard
        includes the MV 

        Hutton oil and gas platform deco mmissioning programme which regarded
        Lophelia 

        pertusa as an opportunist suggesting that this is sufficient reason for
        it not to affect 

        the decommissioning outcome of this facility (British Petroleum, 2006)
        .  With regard 

        to the current development, statutory consultation will be required t o
        confirm 

        requirements within the deco mmissioning p rogramme and to ensure that
        the 

        potential for effects on protected species are properly assessed . 
        There are no 

        records of Lophelia pertusa , or any other protected species likely to
        attach to the 

        turbines, occurring within the vicinity of the proposed wind farms at
        Smith Bank 

        although some records exist of its presence within the Southern Trench
        (see Chapter 

        4.2: Benthic Ecology).  Furthermore, L. pertusa typically occurs at
        depths of greater 

        than 150  m and is rarely found attached to hard substrata (Peckett,
        2003) .  

        Consequently, the likelihood of this species becoming established on the
        turbines 

        within the three proposed wind farm sites is very low. 

        Accidental Spillages of Chemicals 

        7.1.6.48 Accidental spillages or release of chemicals such as grouting,
        fuel and oil during the 

        construction, operation and deco mmissioning phases of the wind farms
        may 

        potentially contaminate seabed sediments .  The severity of this effect
        on benthic 

        ecology depends upon the quantities a nd nature of the spillage  /
        release, the 

        dilution and dispersal properties of the receiving waters and the bio
        –availability of 

        the contaminant to benthic species .  At this stage, the quantities and
        types of 

        material which might conceivably enter the marine  environment in this
        way are not 

        known and so scale and magnitude of effects are unquantifiable at
        present .  In the 

        worst case scenario , the potential significance of an accidental
        spillage would be 

        major.  Accidents are by definition unknown and the uncer tainty
        associated with 

        this effect is therefore high.
      - |-
        212 BIOLOGYOFDEATH
        inwhichtheenvironmentalforces(ofsub-lethalinten-
        sity,ofcourse}chieflyactindeterminingdurationof
        life,appearstolie~bychangingtherateofmetabolismof
        theindividual.Furthermoreonewouldsuggest,ontMs
        view,thatwhathereditydoesinrelationtodurationof
        lifeischieflytodetermine,withinfairlynarrowlimits,
        thetotalenergyoutputwhichtheindividualcanexhibit
        initslifetime.Thislimitationisdirectlybroughtabout
        presumablythroughtwogeneralfactors:viz,(a)the
        kindorqualityofmaterialofwhichthisparticularvital
        machineisbuilt,and(b)themannerinwhichtheparts
        areputtogetherorassembled.Bothofthesefactors
        are,ofcourse,expressionsoftheextentandcharacter
        oftheprocessesoforganicevolutionwhichhavegiven
        risetothisparticularspeciesaboutwhichwemaybe
        talkinginaparticularinstance
        Thereissomedirectexperimentalevidence,smallin
        amounttobesure,butexactandpertinent,totheeffect
        thatthedurationoflifeofananimalstandsininversere-
        lationtothetotalamountofitsmetabolicactivity,orput
        inotherwords,tothework,inthesenseoftheoretical
        mechanics,thatitasamachinedoesduringitslife.
        Slonakerkept4albinoratsincagesliketheoldfashioned
        revolvingsquirrelcages,withaproperlycalibratedodo-
        meterattachedtotheaxle,sothatthetotalamountof
        runningwhichtheydidintheirwholelivescouldbe
        recorded.TheresultswerethoseshowninTable26.
        Itwillbeperceivedthattheamountofexercisetaken
        bytheseratswasastonishinglylarge.Foraratto
        run5,447milesinthecourseofitslifeisindeedare-
        markableperformance.Nowthese4ratsattainedan
        averageageatdeathof29.5months.Butthreecontrol
        ratsconfinedinstationarycagessothattheycouldonly
      - >-
        10.3 Fresnel Approximation 265

        To approximate R in the exponent, we must proceed with caution. To this
        end

        we expand (10.2) under the assumption z2 ≫ (x −x′)2 +(y − y′)2. Again,
        this is

        consistent with the idea of restricting ourselves to relatively small
        angles. The

        expansion of (10.2) is written as

        R = z

        s

        1 + (x −x′)2 +

        ¡

        y − y′¢2

        z2

        ∼= z

        "

        1 +

        ¡

        x −x′¢2 +

        ¡

        y − y′¢2

        2z2 +···

        #

        (exponent; Fresnel approximation) (10.12)

        Substitution of (10.11) and (10.12) into the Huygens-Fresnel diffraction
        formula

        (10.1) yields

        E

        ¡

        x, y, z

        ¢∼= −i ei kz ei k

        2z (x2+y2)

        λz

        Ï

        aperture

        E

        ¡

        x′, y′,0

        ¢

        ei k

        2z (x′2+y′2)e−i k

        z (xx ′+y y′)d x′d y′

        (Fresnel approximation) (10.13)

        This approximation may look a bit messier than before, but in terms of
        being able

        to make progress on integration our chances are somewhat improved.

        Figure 10.8 Field amplitude fol-

        lowing a rectangular aperture com-

        puted in the Fresnel approxima-

        tion.

        Example 10.3

        Compute the Fresnel diffraction field following a rectangular aperture
        (dimensions

        ∆x by ∆y) illuminated by a uniform plane wave.

        Solution: According to (10.13), the field downstream is

        E

        ¡

        x, y, z

        ¢

        = −i E0

        ei kz

        λz ei k

        2z (x2+y2)

        ∆x/2Z

        −∆x/2

        d x′ei k

        2z x′2

        e−i kx

        z x′

        ∆y/2Z

        −∆y/2

        d y′ei k

        2z y′2

        e−i k y

        z y′

        Unfortunately, the integration in the preceding example must be
        performed

        numerically. This is often the case for diffraction integrals in the
        Fresnel approx-

        imation, but at least numerical fast Fourier transforms can aid in the
        process.

        Figure 10.8 shows the result of integration for a rectangular aperture
        with a height

        twice its width.

        Paraxial Wave Equation

        If we assume that the light coming through the aperture is highly
        directional, such

        that it propagates mainly in the z-direction, we are motivated to write
        the field

        as E(x, y, z) = ˜E(x, y, z)ei kz . Upon substitution of this into the
        scalar Helmholtz

        equation (10.5), we arrive at

        ∂2 ˜E

        ∂x2 + ∂2 ˜E

        ∂y2 +2i k∂ ˜E

        ∂z + ∂2 ˜E

        ∂z2 = 0 (10.14)

        At this point we make the paraxial wave approximation,5 which is |2k ∂
        ˜E

        ∂z | ≫ |∂2 ˜E

        ∂z2 |.

        That is, we assume that the amplitude of the field varies slowly in the
        z-direction

        5P . W . Milonni and J. H. Eberly,Laser, Sect. 14.4 (New York: Wiley,
        1988).
  - source_sentence: "with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone's\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n\"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced.\"\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe"
    sentences:
      - >-
        81

        13.13 RODLESS CYLINDERS

        The rodless cylinder is a device that requires particular attention
        whenever used, 

        because in contrast to the traditional cylinders, where the load is
        placed in line with 

        the rod, in the rodless cylinder the weight is anchored on a carriage
        that runs on the 

        top part of the cylinder, and between the cylinder axis and the load’s
        barycentre there 

        is always a more or less accentuated arm according to the shape of the
        object to be 

        moved.    

        The piston’s force is transmitted to an external carriage by a mechanic
        arm that comes 

        out from an opening located in the barrel along the entire stroke and is
        connected to 

        the piston solidly. Sealing is guaranteed by an internal metallic strap
        fixed at the ends 

        of the body that completely covers the opening. The piston’s gaskets,
        their internal 

        pressure and a magnetic band properly positioned make the metallic plate
        adhere to 

        the internal surface of the tube, ensuring sufficient outward sealing
        and also between 

        the two cylinder chambers.

        A further metallic strap placed outside, in correspondence with the
        opening, prevents 

        dust collection in the sliding areas. Sealing in this type of cylinder
        is never perfect. Par-

        ticular guide systems obtained on the carriage and on the piston, open
        the two plates 

        in order to allow mechanic connection between piston and slider/cursor.
        In opposition 

        to rod cylinders, the forces expressed by the cylinder in the two
        directions are identi-

        cal. In fact, there is no difference in sections on the two sides of the
        piston since the 

        rod does not exist. The regulating air-cushion absorption function is
        exactly identical 

        to the one performed in the rod cylinders.
         96 
         
         
        In realtà gli in gombri totali del cilindro compatto sono superioni
        rispetto al cilindro a 

        corsa breve, per questo motivo  le due versioni sono tuttora presenti
        sul mercato  e l’uno 

        non sostituisce l’altro. 

        Il cilindro compatto, al contrario del corsa breve, viene sviluppato 
        sin dall’inizio 

        seguendo, per scelta del primo produttore che lo realizzò, gli ingombri
        imposti dall’ente 

        nazionale di unificazione francese (UNITOP) e quindi esiste intercambia
        bilità tra 

        differenti produttori. 

        Alcuni di questi produttori hanno inserito anche una versione ISO che
        unifica di fatto le 

        quote di fissaggio degli accessori utilizzabili quindi in differenti
        serie di cilindri. 

        Tutto ciò consente all’utilizzatore finale di razionalizzare il proprio
        magazzino. 
         
        13.13  Cilindri senza stelo 
         
        Il cilind ro senza stelo è un apparecchio che merita particolare
        attenzione quando 

        applicato, perché al contrario dei cilindri tradizionali in cui il
        carico è posi zionato in 

        asse con lo stelo, nel cilindro senza stelo il peso viene ancorato su di
        un carrello che 

        scorre sulla parte superiore dello stesso e, tra asse del cilindro e
        baricentro del carico, vi 

        è sempre un braccio più o meno accentuato a seconda della forma
        dell’oggetto da  

        movimentare.      
         
          
                                                                                                              
         
         
         
         
         
                                                                                                   
         
         
         
          
         
         
         
         
        Chapter 13

        Pneumatic devices 

        Pneumatic Guide_GB.indd   81 15/04/2015   08:46:21
      - >-
        4.2 Density operators and normal states 109

        4.2 Density operators and normal states

        Deﬁnition 2.4 of a state still makes good sense in the
        inﬁnite-dimensional case, as

        it simply specializes the general deﬁnition of a state on a C*-algebra A
        to the case

        A = B(H). Thus we continue to say that a state on B(H) is a
        complex-linear map

        ω : B(H) →C satisfying ω(b∗b) ≥0 for each b ∈B(H) and ω(1H )= 1. Despite

        this lack of novelty in the deﬁnition of a state (i.e., compared to
        ﬁnite-dimensional

        Hilbert spaces), Theorem 2.7 no longer holds if H is
        inﬁnite-dimensional: although

        it (almost trivially) remains true that density operatorsρ on H deﬁne
        states on B(H)

        through the fundamental correspondenceω(a)= Tr(ρa), a ∈B(H), cf. (2.33),
        there

        are (many) states that are not given in that way (see below).
        Fortunately, states that

        do arise through (2.33) can be characterized in a simple way.

        Deﬁnition 4.11. A state ω : B(H) →C is called normal if for each
        orthogonal

        family (ei) of projections (i.e., e∗

        i = ei and eiej = δij ei) one has

        ω

        (

        ∑

        i

        ei

        )

        = ∑

        i

        ω(ei). (4.28)

        Here ∑i ei is deﬁned as the projection on the smallest closed subspace K
        of H that

        contains each eiH (that is, ∑i ei = ∨iei, i.e., the supremum in the
        poset P(H) of all

        projections on H with respect to the partial order e≤fi f f e H⊆f H).
        Furthermore,

        the sum over i on the right-hand side is deﬁned by (B.11), i.e., as the
        supremum (in

        R) of the set of all sums ∑i∈F ω(ei) over ﬁnite subsets F ⊂I of the
        index set I in

        which i takes values. It is ﬁnite because∑i∈F ei ≤1H and hence, since ω
        is positive,

        ∑

        i∈F

        ω(ei) ≤ω(1H )= 1.

        For example, let(υi) be a basis ofH with associated one-dimensional
        projections

        ei = |υi⟩⟨υi|. (4.29)

        If ω is assumed to be a state, then the additivity condition (4.28)
        implies

        ∑

        i

        ω(ei)= 1, (4.30)

        or, equivalently, using Deﬁnition B.6 etc. as well as the notationeF
        ≡∑i∈F ei,

        lim

        F

        ω(eF )= 1. (4.31)

        If H is separable, any orthogonal family (ei) of projections is
        necessarily countable,

        and (4.28) is analogous to the countable additivity condition deﬁning a
        measure.

        Theorem 4.12. A state ω on B(H) takes the form ω(a)= Tr(ρa) for some
        (unique)

        density operator ρ ∈D(H) iff it is normal.
      - >-
        C.9 Ideals in C*-algebras 675

        by Deﬁnition C.35 and the proof of Proposition C.51. The second term on
        the right-

        hand side goes to zero for λ →∞, since j ∈J. Hence

        lim

        λ→∞

        ∥a −a1λ∥≤∥ a + j∥. (C.115)

        For each ε > 0 we can choose j ∈J so that (C.102) holds. For this
        speciﬁc j,w e

        combine (C.112), (C.115), and (C.102) to ﬁnd

        lim

        λ→∞

        ∥a −a1λ∥−ε ≤∥τ(a)∥≤∥ a −a1λ∥. (C.116)

        Letting ε →0 proves (C.111). □

        We now prove (C.2) in A/J. Successively using (C.111), (C.2) in ˙A,
        (C.114),

        (C.111), (C.99), and (C.110), we ﬁnd

        ∥τ(a)∥2 = lim

        λ→∞

        ∥a −a1λ∥2 = lim

        λ→∞

        ∥(a −a1λ)∗(a −a1λ)∥

        = lim

        λ→∞

        ∥(1A −1λ)a∗a(1A −1λ)∥≤ lim

        λ→∞

        ∥1 −1λ∥∥a∗a(1A −1λ)∥

        ≤ lim

        λ→∞

        ∥a∗a(1A −1λ)∥= ∥τ(a∗a)∥= ∥τ(a)τ(a∗)∥

        = ∥τ(a)τ(a)∗∥. (C.117)

        As in the proof of Proposition C.30, this implies (C.2), and hence
        Theorem C.60.□

        We now state and prove the key result about morphisms.

        Theorem C.62. Let α : A →B be a nonzero homomorphism between
        C*-algebras.

        1. The homomorphism α is continuous, with norm ∥α∥= 1.

        2. Its kernel ker(α) is an ideal in A.

        3. If α is injective, then it is isometric.

        4. An isomorphism of C*-algebras is automatically isometric.

        5. The rangeα(A) is a C*-subalgebra of B; in particular,α(A) is closed
        in B.

        Proof. If necessary, we ﬁrst reduce the proof of the ﬁrst claim to the
        case where

        A and B have units and α is unital: we do so by replacing A and B by ˙A
        and ˙B,

        respectively (even if A and/or B was already unital in the ﬁrst place,
        but α was not),

        and replacing α by the homomorphism ˙α : ˙A → ˙B deﬁned in (C.66). If we
        do so,

        it follows from Lemma C.34 that in the worst case the spectrum of a or
        α(a) is

        modiﬁed by adding 0, which does not change the spectral radius.
        Therefore, the

        move fromα to ˙α makes no difference to the argument to follow, so we
        assume

        that 1A ∈A and 1B ∈B, and α(1A)= 1B.I f z ∈ρ(a), so that (a −z)−1 exists
        in

        A, then α(a −z) is certainly invertible in B, for (C.4) implies that
        (α(a −z))−1 =

        α((a −z)−1). Hence ρ(a) ⊆ρ(α(a)), so that

        σ(α(a)) ⊆σ(a). (C.118)

        Replacing a by a∗a this gives r(α(a∗a)) ≤r(a∗a), and since α(a∗a)=
        α(a)∗α(a),

        eq. (C.55) yields ∥α(a)∥≤∥a∥, and hence ∥α∥≤ 1. This proves continuity
        of α.
  - source_sentence: "with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone's\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n\"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced.\"\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe"
    sentences:
      - >-
        31 
         
         
        2.Chapter Two:………………………………………………………….. Causes of Aging 
         
         
         There are many types of free radicals and the most related to the 
        biological process are those which derived from oxygen: the  Reactive 

        Oxygen Species ( ROS ). These ROS include superoxide anion , peroxide 

        and hydro radicals . ROS are produced in vivo within the mitochondria 

        during electron tra nsport chain. They are also produced as
        intermediate 

        products in different enzymatic reactions and by different
        physiological 

        processes such as: 

         Phagocytic activity of white blood cells, specifically neu trophils. 

        Neutrophils generate ROS during phagocytic activity in order to kill
        the 

        invading pathogens as a host defense mechanism. 
         
         When the cells are exposed to abnormal conditions -such as hypoxia 

        or hperoxia -produce ROS. Some drugs have the ability to induce the 

        cells to produce ROS due to their oxidizing effect. 
         
         An exposure to radiation may induce the biological systems to 

        produce ROS.
      - "Figure 4.2: Particle plots of the dark matter density in cold dark matter\ndominated models. The simulation box is 240Mpc/h on a side, the thickness\nof the shown slices is around 8Mpc/h. The particle distribution is very\n\flamentary, a consequence of the large amount of large scale power in this\nmodel. The higher density \flaments delineate nearly spherical under dense\nvoids. Very high density haloes occur on the intersection between \flaments.\nDi\verent redshifts (z = 3, 1, 0) are shown from left to right. Plots from top to\nbottom are (1) a Universe with cosmological constant (\n m = 0:3;\n\x03 = 0:3),\n(2) Einstein-de Sitter Universe (\n m = 1:0;\n\x03 = 0:0), (3) a cosmology with\na tilted power-spectrum (\n m = 1:0;\n\x03 = 0:0), (4) an \n m = 0:3 Open model\n(\nm = 0:3;\n\x03 = 0:0). (Jenkins et al, 1998 Astrophysical Journal,499,20-40)\n79"
      - |-
        THEINHERITANCEOFDURATION177
        preferredtostatetheconclusionintermsofdeath,rates,
        asitwasoriginallystatedbyPearson,becauseofthe
        bearingithasuponagreatdealofthepublichealth
        propagandasolooselyflungabout.Itneedonlybere-
        memberedthatthereisaperfectlydefinitefunctional
        relationbetweendeathrateandaveragedurationoflife
        inanapproximatelystablepopulationgroup,expres-
        siblebyanequation,inordertoseethatanyconclusion
        astotherelativeinfluenceofheredityandenvironment
        uponthegeneraldeathratemustapplywithequalforce
        tothedurationoflife.
        THESELECTIVEDEATHBATEINMAN
        Ifthedurationo; lifewereinheriteditwouldlogical-
        lybeexpectedthatsomeportionofthedeathratemust
        beselectiveincharacter.Forinheritanceofduration
        oflifecanonlymeanthatwhenapersondiesisinpart
        determinedbythatindividual'sbiologicalconstitutionor
        makeup.Andequallyitisobviousthatindividualsof
        weakandunsoundconstitutionmust,ontheaverage,
        dieearlierthanthoseofstrong,sound,andvigorouscon-
        stitution."Whenceitfollowsthatthechancesofleaving
        offspringwillbegreaterforthoseofsoundconstitution
        thanfortheweaklings.Themathematicaldiscussion
        whichhasjustbeengivenindicatesthatfromone-half
        tothree-fourthsofthedeathrateisselectiveinchar-
        acter,becausethatproportionisdeterminedbyhereditary
        factors.Justinproportionashereditydetermines
        thedeathrate,soisthemortalityselective.Therealityof
        thefactofaselectivedeathrateinmancanbeeasily
        showngraphically.
        InFigure44areseenthegraphsofsomedatafrom
        Europeanroyalfamilies,wherenoneglectofchildren,
        12
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
  - cosine_accuracy
  - cosine_accuracy_threshold
  - cosine_f1
  - cosine_f1_threshold
  - cosine_precision
  - cosine_recall
  - cosine_ap
  - cosine_mcc
model-index:
  - name: SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2
    results:
      - task:
          type: binary-classification
          name: Binary Classification
        dataset:
          name: Unknown
          type: unknown
        metrics:
          - type: cosine_accuracy
            value: 0.7934
            name: Cosine Accuracy
          - type: cosine_accuracy_threshold
            value: 0.14760157465934753
            name: Cosine Accuracy Threshold
          - type: cosine_f1
            value: 0.6493108728943339
            name: Cosine F1
          - type: cosine_f1_threshold
            value: 0.10666096210479736
            name: Cosine F1 Threshold
          - type: cosine_precision
            value: 0.654320987654321
            name: Cosine Precision
          - type: cosine_recall
            value: 0.6443768996960486
            name: Cosine Recall
          - type: cosine_ap
            value: 0.7384230309954641
            name: Cosine Ap
          - type: cosine_mcc
            value: 0.4793492257096312
            name: Cosine Mcc

SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2

This is a sentence-transformers model finetuned from sentence-transformers/all-MiniLM-L6-v2. It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

Model Details

Model Description

Model Type: Sentence Transformer
Base model: sentence-transformers/all-MiniLM-L6-v2
Maximum Sequence Length: 256 tokens
Output Dimensionality: 384 dimensions
Similarity Function: Cosine Similarity

Model Sources

Documentation: Sentence Transformers Documentation
Repository: Sentence Transformers on GitHub
Hugging Face: Sentence Transformers on Hugging Face

Full Model Architecture

SentenceTransformer(
  (0): Transformer({'max_seq_length': 256, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): Normalize()
)

Usage

Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("Chandar/sv-subject-based-all-MiniLM-L6-v2")
# Run inference
sentences = [
    'with\tthe\torigin\tof\tthe\tcoal\tformed\tduring\tthe\tcarboniferous\tepoch,\ttwo\tor\tthree\nconsiderations\tsuggest\tthemselves.\nIn\tthe\tfirst\tplace,\tthe\tgreat\tphantom\tof\tgeological\ttime\trises\tbefore\tthe\tstudent\tof\nthis,\tas\tof\tall\tother,\tfragments\tof\tthe\thistory\tof\tour\tearth—\tspringing\nirrepressibly\tout\tof\tthe\tfacts,\tlike\tthe\tDjin\tfrom\tthe\tjar\twhich\tthe\tfishermen\tso\nincautiously\topened;\tand\tlike\tthe\tDjin\tagain,\tbeing\tvaporous,\tshifting,\tand\nindefinable,\tbut\tunmistakably\tgigantic.\tHowever\tmodest\tthe\tbases\tof\tone\'s\ncalculation\tmay\tbe,\tthe\tminimum\tof\ttime\tassignable\tto\tthe\tcoal\tperiod\tremains\nsomething\tstupendous.\nPrincipal\tDawson\tis\tthe\tlast\tperson\tlikely\tto\tbe\tguilty\tof\texaggeration\tin\tthis\nmatter,\tand\tit\twill\tbe\twell\tto\tconsider\twhat\the\thas\tto\tsay\tabout\tit:—\n"The\trate\tof\taccumulation\tof\tcoal\twas\tvery\tslow.\tThe\tclimate\tof\tthe\tperiod,\tin\nthe\tnorthern\ttemperate\tzone,\twas\tof\tsuch\ta\tcharacter\tthat\tthe\ttrue\tconifers\tshow\nrings\tof\tgrowth,\tnot\tlarger,\tnor\tmuch\tless\tdistinct,\tthan\tthose\tof\tmany\tof\ttheir\nmodern\tcongeners.\tThe\t\nSigillarioe\n\tand\t\nCalamites\n\twere\tnot,\tas\toften\tsupposed,\ncomposed\twholly,\tor\teven\tprincipally,\tof\tlax\tand\tsoft\ttissues,\tor\tnecessarily\nshort-lived.\tThe\tformer\thad,\tit\tis\ttrue,\ta\tvery\tthick\tinner\tbark;\tbut\ttheir\tdense\nwoody\taxis,\ttheir\tthick\tand\tnearly\timperishable\touter\tbark,\tand\ttheir\tscanty\tand\nrigid\tfoliage,\twould\tindicate\tno\tvery\trapid\tgrowth\tor\tdecay.\tIn\tthe\tcase\tof\tthe\nSigillarioe\n,\tthe\tvariations\tin\tthe\tleaf-scars\tin\tdifferent\tparts\tof\tthe\ttrunk,\tthe\nintercalation\tof\tnew\tridges\tat\tthe\tsurface\trepresenting\tthat\tof\tnew\twoody\twedges\nin\tthe\taxis,\tthe\ttransverse\tmarks\tleft\tby\tthe\tstages\tof\tupward\tgrowth,\tall\tindicate\nthat\tseveral\tyears\tmust\thave\tbeen\trequired\tfor\tthe\tgrowth\tof\tstems\tof\tmoderate\nsize.\tThe\tenormous\troots\tof\tthese\ttrees,\tand\tthe\tcondition\tof\tthe\tcoal-swamps,\nmust\thave\texempted\tthem\tfrom\tthe\tdanger\tof\tbeing\toverthrown\tby\tviolence.\nThey\tprobably\tfell\tin\tsuccessive\tgenerations\tfrom\tnatural\tdecay;\tand\tmaking\nevery\tallowance\tfor\tother\tmaterials,\twe\tmay\tsafely\tassert\tthat\tevery\tfoot\tof\nthickness\tof\tpure\tbituminous\tcoal\timplies\tthe\tquiet\tgrowth\tand\tfall\tof\tat\tleast\nfifty\tgenerations\tof\t\nSigillarioe\n,\tand\ttherefore\tan\tundisturbed\tcondition\tof\tforest\ngrowth\tenduring\tthrough\tmany\tcenturies.\tFurther,\tthere\tis\tevidence\tthat\tan\nimmense\tamount\tof\tloose\tparenchymatous\ttissue,\tand\teven\tof\twood,\tperished\tby\ndecay,\tand\twe\tdo\tnot\tknow\tto\twhat\textent\teven\tthe\tmost\tdurable\ttissues\tmay\nhave\tdisappeared\tin\tthis\tway;\tso\tthat,\tin\tmany\tcoal-seams,\twe\tmay\thave\tonly\ta\nvery\tsmall\tpart\tof\tthe\tvegetable\tmatter\tproduced."\nUndoubtedly\tthe\tforce\tof\tthese\treflections\tis\tnot\tdiminished\twhen\tthe',
    '31 \n \n \n2.Chapter Two:………………………………………………………….. Causes of Aging \n \n \n There are many types of free radicals and the most related to the \nbiological process are those which derived from oxygen: the  Reactive \nOxygen Species ( ROS ). These ROS include superoxide anion , peroxide \nand hydro radicals . ROS are produced in vivo within the mitochondria \nduring electron tra nsport chain. They are also produced as intermediate \nproducts in different enzymatic reactions and by different physiological \nprocesses such as: \n\uf0a7 Phagocytic activity of white blood cells, specifically neu trophils. \nNeutrophils generate ROS during phagocytic activity in order to kill the \ninvading pathogens as a host defense mechanism. \n \n\uf0a7 When the cells are exposed to abnormal conditions -such as hypoxia \nor hperoxia -produce ROS. Some drugs have the ability to induce the \ncells to produce ROS due to their oxidizing effect. \n \n\uf0a7 An exposure to radiation may induce the biological systems to \nproduce ROS.',
    'THEINHERITANCEOFDURATION177\npreferredtostatetheconclusionintermsofdeath,rates,\nasitwasoriginallystatedbyPearson,becauseofthe\nbearingithasuponagreatdealofthepublichealth\npropagandasolooselyflungabout.Itneedonlybere-\nmemberedthatthereisaperfectlydefinitefunctional\nrelationbetweendeathrateandaveragedurationoflife\ninanapproximatelystablepopulationgroup,expres-\nsiblebyanequation,inordertoseethatanyconclusion\nastotherelativeinfluenceofheredityandenvironment\nuponthegeneraldeathratemustapplywithequalforce\ntothedurationoflife.\nTHESELECTIVEDEATHBATEINMAN\nIfthedurationo; lifewereinheriteditwouldlogical-\nlybeexpectedthatsomeportionofthedeathratemust\nbeselectiveincharacter.Forinheritanceofduration\noflifecanonlymeanthatwhenapersondiesisinpart\ndeterminedbythatindividual\'sbiologicalconstitutionor\nmakeup.Andequallyitisobviousthatindividualsof\nweakandunsoundconstitutionmust,ontheaverage,\ndieearlierthanthoseofstrong,sound,andvigorouscon-\nstitution."Whenceitfollowsthatthechancesofleaving\noffspringwillbegreaterforthoseofsoundconstitution\nthanfortheweaklings.Themathematicaldiscussion\nwhichhasjustbeengivenindicatesthatfromone-half\ntothree-fourthsofthedeathrateisselectiveinchar-\nacter,becausethatproportionisdeterminedbyhereditary\nfactors.Justinproportionashereditydetermines\nthedeathrate,soisthemortalityselective.Therealityof\nthefactofaselectivedeathrateinmancanbeeasily\nshowngraphically.\nInFigure44areseenthegraphsofsomedatafrom\nEuropeanroyalfamilies,wherenoneglectofchildren,\n12',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]

Evaluation

Metrics

Binary Classification

Evaluated with BinaryClassificationEvaluator

Metric	Value
cosine_accuracy	0.7934
cosine_accuracy_threshold	0.1476
cosine_f1	0.6493
cosine_f1_threshold	0.1067
cosine_precision	0.6543
cosine_recall	0.6444
cosine_ap	0.7384
cosine_mcc	0.4793

Training Details

Training Dataset

Unnamed Dataset

Size: 1,124,250 training samples
Columns: sentence1, sentence2, and label
Approximate statistics based on the first 1000 samples:
sentence1 sentence2 label
type string string int
details
min: 256 tokens
mean: 256.0 tokens
max: 256 tokens

min: 23 tokens
mean: 242.22 tokens
max: 256 tokens

0: ~50.10%
1: ~49.90%

	sentence1	sentence2	label
type	string	string	int
details	min: 256 tokens mean: 256.0 tokens max: 256 tokens	min: 23 tokens mean: 242.22 tokens max: 256 tokens	0: ~50.10% 1: ~49.90%

Samples:

sentence1	sentence2	label
with the origin of the coal formed during the carboniferous epoch, two or three considerations suggest themselves. In the first place, the great phantom of geological time rises before the student of this, as of all other, fragments of the history of our earth— springing irrepressibly out of the facts, like the Djin from the jar which the fishermen so incautiously opened; and like the Djin again, being vaporous, shifting, and indefinable, but unmistakably gigantic. However modest the bases of one's calculation may be, the minimum of time assignable to the coal period remains something stupendous. Principal Dawson is the last person likely to be guilty of exaggeration in this matter, and it will be well to consider what he has to say about it:— "The rate of accumulation of coal was very slow. The climate of the period, in the northern temperate zone, was of such a character that the true conifers show rings of growth, not larger, nor much less distinct, than those of many of their moder...	organic coenzymes to catalyze its specific chemical reaction. Therefore, enzyme function is, in part, regulated by an abundance of various cofactors and coenzymes, which are supplied primarily by the diets of most organisms. Figure 6.20Vitamins are important coenzymes or precursors of coenzymes, and are required for enzymes to function properly. Multivitamin capsules usually contain mixtures of all the vitamins at different percentages. Enzyme Compartmentalization In eukaryotic cells, molecules such as enzymes are usually compartmentalized into different organelles. This allows for yet another level of regulation of enzyme activity. Enzymes required only for certain cellular processes can be housed separately along with their substrates, allowing for more efficient chemical reactions. Examples of this sort of enzyme regulation based on location and proximity include the enzymes involved in the latter stages of cellular respiration, which take place exclusively in the mitochondria, and ...	`1`
with the origin of the coal formed during the carboniferous epoch, two or three considerations suggest themselves. In the first place, the great phantom of geological time rises before the student of this, as of all other, fragments of the history of our earth— springing irrepressibly out of the facts, like the Djin from the jar which the fishermen so incautiously opened; and like the Djin again, being vaporous, shifting, and indefinable, but unmistakably gigantic. However modest the bases of one's calculation may be, the minimum of time assignable to the coal period remains something stupendous. Principal Dawson is the last person likely to be guilty of exaggeration in this matter, and it will be well to consider what he has to say about it:— "The rate of accumulation of coal was very slow. The climate of the period, in the northern temperate zone, was of such a character that the true conifers show rings of growth, not larger, nor much less distinct, than those of many of their moder...	Infertility Infertility is the inability to conceive a child or carry a child to birth. About 75 percent of causes of infertility can be identified; these include diseases, such as sexually transmitted diseases that can cause scarring of the reproductive tubes in either men or women, or developmental problems frequently related to abnormal hormone levels in one of the individuals. Inadequate nutrition, especially starvation, can delay menstruation. Stress can also lead to infertility. Short-term stress can affect hormone levels, while long-term stress can delay puberty and cause less frequent menstrual cycles. Other factors that affect fertility include toxins (such as cadmium), tobacco smoking, marijuana use, gonadal injuries, and aging. If infertility is identified, several assisted reproductive technologies (ART) are available to aid conception. A common type of ART isin vitrofertilization (IVF) where an egg and sperm are combined outside the body and then placed in the uterus. Eggs...	`1`
with the origin of the coal formed during the carboniferous epoch, two or three considerations suggest themselves. In the first place, the great phantom of geological time rises before the student of this, as of all other, fragments of the history of our earth— springing irrepressibly out of the facts, like the Djin from the jar which the fishermen so incautiously opened; and like the Djin again, being vaporous, shifting, and indefinable, but unmistakably gigantic. However modest the bases of one's calculation may be, the minimum of time assignable to the coal period remains something stupendous. Principal Dawson is the last person likely to be guilty of exaggeration in this matter, and it will be well to consider what he has to say about it:— "The rate of accumulation of coal was very slow. The climate of the period, in the northern temperate zone, was of such a character that the true conifers show rings of growth, not larger, nor much less distinct, than those of many of their moder...	Figure 18.13The honeycreeper birds illustrate adaptive radiation. From one original species of bird, multiple others evolved, each with its own distinctive characteristics. Notice the differences in the species’ beaks in Figure 18.13. Evolution in response to natural selection based on specific food sources in each new habitat led to evolution of a different beak suited to the specific food source. The seed-eating bird has a thicker, stronger beak which is suited to break hard nuts. The nectar-eating birds have long beaks to dip into flowers to reach the nectar. The insect-eating birds have beaks like swords, appropriate for stabbing and impaling insects. Darwin’s finches are another example of adaptive radiation in an archipelago. Click through this interactive site (http://openstaxcollege.org/l/bird_evolution) to see how island birds evolved in evolutionary increments from 5 million years ago to today. Sympatric Speciation Can divergence occur if no physical barriers are in place to ...	`1`

Loss: CoSENTLoss with these parameters:

{
    "scale": 20.0,
    "similarity_fct": "pairwise_cos_sim"
}

Training Hyperparameters

Non-Default Hyperparameters

per_device_train_batch_size: 16
per_device_eval_batch_size: 32
learning_rate: 2e-05
weight_decay: 0.01
max_steps: 2000

All Hyperparameters

Click to expand

overwrite_output_dir: False
do_predict: False
eval_strategy: no
prediction_loss_only: True
per_device_train_batch_size: 16
per_device_eval_batch_size: 32
per_gpu_train_batch_size: None
per_gpu_eval_batch_size: None
gradient_accumulation_steps: 1
eval_accumulation_steps: None
torch_empty_cache_steps: None
learning_rate: 2e-05
weight_decay: 0.01
adam_beta1: 0.9
adam_beta2: 0.999
adam_epsilon: 1e-08
max_grad_norm: 1.0
num_train_epochs: 3.0
max_steps: 2000
lr_scheduler_type: linear
lr_scheduler_kwargs: {}
warmup_ratio: 0.0
warmup_steps: 0
log_level: passive
log_level_replica: warning
log_on_each_node: True
logging_nan_inf_filter: True
save_safetensors: True
save_on_each_node: False
save_only_model: False
restore_callback_states_from_checkpoint: False
no_cuda: False
use_cpu: False
use_mps_device: False
seed: 42
data_seed: None
jit_mode_eval: False
use_ipex: False
bf16: False
fp16: False
fp16_opt_level: O1
half_precision_backend: auto
bf16_full_eval: False
fp16_full_eval: False
tf32: None
local_rank: 0
ddp_backend: None
tpu_num_cores: None
tpu_metrics_debug: False
debug: []
dataloader_drop_last: False
dataloader_num_workers: 0
dataloader_prefetch_factor: None
past_index: -1
disable_tqdm: False
remove_unused_columns: True
label_names: None
load_best_model_at_end: False
ignore_data_skip: False
fsdp: []
fsdp_min_num_params: 0
fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
fsdp_transformer_layer_cls_to_wrap: None
accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
deepspeed: None
label_smoothing_factor: 0.0
optim: adamw_torch
optim_args: None
adafactor: False
group_by_length: False
length_column_name: length
ddp_find_unused_parameters: None
ddp_bucket_cap_mb: None
ddp_broadcast_buffers: False
dataloader_pin_memory: True
dataloader_persistent_workers: False
skip_memory_metrics: True
use_legacy_prediction_loop: False
push_to_hub: False
resume_from_checkpoint: None
hub_model_id: None
hub_strategy: every_save
hub_private_repo: None
hub_always_push: False
hub_revision: None
gradient_checkpointing: False
gradient_checkpointing_kwargs: None
include_inputs_for_metrics: False
include_for_metrics: []
eval_do_concat_batches: True
fp16_backend: auto
push_to_hub_model_id: None
push_to_hub_organization: None
mp_parameters:
auto_find_batch_size: False
full_determinism: False
torchdynamo: None
ray_scope: last
ddp_timeout: 1800
torch_compile: False
torch_compile_backend: None
torch_compile_mode: None
include_tokens_per_second: False
include_num_input_tokens_seen: False
neftune_noise_alpha: None
optim_target_modules: None
batch_eval_metrics: False
eval_on_start: False
use_liger_kernel: False
liger_kernel_config: None
eval_use_gather_object: False
average_tokens_across_devices: False
prompts: None
batch_sampler: batch_sampler
multi_dataset_batch_sampler: proportional

Training Logs

Epoch	Step	Training Loss	cosine_ap
-1	-1	-	0.7384
0.0071	500	0.5524	-
0.0142	1000	0.0016	-
0.0213	1500	0.0004	-
0.0285	2000	0.0001	-

Framework Versions

Python: 3.12.9
Sentence Transformers: 4.1.0
Transformers: 4.53.0
PyTorch: 2.7.1
Accelerate: 1.8.1
Datasets: 3.6.0
Tokenizers: 0.21.2

Citation

BibTeX

Sentence Transformers

@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}

CoSENTLoss

@online{kexuefm-8847,
    title={CoSENT: A more efficient sentence vector scheme than Sentence-BERT},
    author={Su Jianlin},
    year={2022},
    month={Jan},
    url={https://kexue.fm/archives/8847},
}