text:
"""
 -----------------------------------------------------------------------------
 Copyright (c) 2009-2017, Shotgun Software Inc

 Redistribution and use in source and binary forms, with or without
 modification, are permitted provided that the following conditions are met:

  - Redistributions of source code must retain the above copyright notice, this
    list of conditions and the following disclaimer.

  - Redistributions in binary form must reproduce the above copyright notice,
    this list of conditions and the following disclaimer in the documentation
    and/or other materials provided with the distribution.

  - Neither the name of the Shotgun Software Inc nor the names of its
    contributors may be used to endorse or promote products derived from this
    software without specific prior written permission.

 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
 FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

-----------------------------------------------------------------------------
"""

from ..six.moves import cPickle as pickle
import os

from .errors import MockgunError

class SchemaFactory(object):
    """
    Allows to instantiate a pickled schema.
    """

    _schema_entity_cache = None
    _schema_entity_cache_path = None
    _schema_cache = None
    _schema_cache_path = None

    @classmethod
    def get_schemas(cls, schema_path, schema_entity_path):
        """
        Retrieves the schemas from disk.

        :param str schema_path: Path to the schema.
        :param str schema_entity_path: Path to the entities schema.

        :returns: Pair of dictionaries holding the schema and entities schema.
        :rtype: tuple
        """
        if not os.path.exists(schema_path):
            raise MockgunError("Cannot locate Mockgun schema file '%s'!" % schema_path)

        if not os.path.exists(schema_entity_path):
            raise MockgunError("Cannot locate Mockgun schema file '%s'!" % schema_entity_path)

        # Poor man's attempt at a cache. All of our use cases deal with a single pair of files
        # for the duration of the unit tests, so keep a cache for both inputs. We don't want
        # to deal with ever growing caches anyway. Just having this simple cache has shown
        # speed increases of up to 500% for Toolkit unit tests alone.

        if schema_path != cls._schema_cache_path:
            cls._schema_cache = cls._read_file(schema_path)
            cls._schema_cache_path = schema_path

        if schema_entity_path != cls._schema_entity_cache_path:
            cls._schema_entity_cache = cls._read_file(schema_entity_path)
            cls._schema_entity_cache_path = schema_entity_path

        return cls._schema_cache, cls._schema_entity_cache

    @classmethod
    def _read_file(cls, path):
        with open(path, "rb") as fh:
            return pickle.load(fh)

# Highest protocol that Python 2.4 supports, which is the earliest version of Python we support.
# Actually, this is the same version that Python 2.7 supports at the moment!
_HIGHEST_24_PICKLE_PROTOCOL = 2

# ----------------------------------------------------------------------------
# Utility methods
def generate_schema(shotgun, schema_file_path, schema_entity_file_path):
    """
    Helper method for mockgun.
    Generates the schema files needed by the mocker by connecting to a real shotgun
    and downloading the schema information for that site. Once the generated schema
    files are being passed to mockgun, it will mimic the site's schema structure.

    :param sg_url: Shotgun site url
    :param sg_script: Script name to connect with
    :param sg_key: Script key to connect with
    :param schema_file_path: Path where to write the main schema file to
    :param schema_entity_file_path: Path where to write the entity schema file to
    """

    schema = shotgun.schema_read()
    fh = open(schema_file_path, "wb")
    try:
        pickle.dump(schema, fh, protocol=_HIGHEST_24_PICKLE_PROTOCOL)
    finally:
        fh.close()

    schema_entity = shotgun.schema_entity_read()
    fh = open(schema_entity_file_path, "wb")
    try:
        pickle.dump(schema_entity, fh, protocol=_HIGHEST_24_PICKLE_PROTOCOL)
    finally:
        fh.close()


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text:
Since Tri-Solfen® was commercially launched, over 80 million lambs have been treated and over 80% of Australian wool growers are now using Tri-Solfen for their sheep. Here's what some of them have to say…
'We have used pain relief for two years now and seen real production gains. We are concerned for the welfare of our animals and will continue to use pain relief to ensure they get the best care.'
Clinton Wise– Wililoo Merino Stud, Woodanilling, W.A.
'It easy to see the difference pain relief makes. Before, lambs would walk away hunched up, even taking a couple of hours to walk back to the paddock. Now they run straight back to Mum and start suckling," says Rod. "My wool is now sold under the Better Choices brand. I see this as a definite advantage. I think it will be an advantage in the long run, to both me and the industry as a whole.'
Rod Miller– Glenpaen Merino Stud, Horsham, Vic
'After being treated with pain relief my lambs were more content and less stressed. As farmers we are sincere in looking after the welfare of our animals and using pain relief demonstrates this.'
Richard Coole– Frankland, W.A.
'We have been using pain relief for the past three years. We're impressed by reduced bleeding in the mulesing wound immediately after application. Lambs run straight back to find the ewe, which has dramatically reduced our mortality rates. Flock management, post lamb marking is easier due to the effect of pain relief and the scab healing faster.'
Ryan & Malcom O'Dea– Peepingee Merino Stud, Narrogin, W.A.
'Using pain relief eases the stress and allows lambs to mother up and move back to the paddock easier with faster weight gains.'
Kent Lummis– Waverley Downs, Gilgandra, NSW
Australia Sheep Granted
Australia Horses, Dogs, Lab animals Granted
Australia Cattle Granted
Australia Humans Granted
Zealand Sheep,
Cattle Granted
Zealand Horses, Dogs, Lab animals Granted
EU Humans Granted
EU Pig, Sheep,
USA Dogs, Horses, Lab animals Granted
USA Humans Granted
USA Pig, Sheep,
Canada Horses, Dogs, Lab animals Granted
Canada Cattle,
Pig Granted
Canada Humans Granted
Non-Executive Director
Ian is Chief Executive Officer of Dechra Pharmaceuticals, which has a 33% shareholder in Medical Ethics. He joined National Veterinary Services, Dechra's former services business in 1989 and joined the Board of Dechra in 1997. In October 2010, Ian was appointed as Non-Executive Chairman of Sanford DeLand Asset Management.
Dr Chris Roberts
Human Wound and Regulatory Advisor
Chris has over 20 years' line management experience of heading clinical research teams. He was previously global head of Smith & Nephew clinical support and market development, where he managed global clinical Phase II and III programmes in the management of venous and pressure ulcers.
Lieutenant Colonel Professor Steven Jeffery
Medical Specialist Advisor
Steve has over 15 years' experience in military plastic surgery. In 2011 he was awarded the Military Civilian Partnership Award for 'Regular of the Year', as well as receiving the Wounds UK 'Key Contribution' award and the Smith and Nephew 'Customer Pioneer of the Year' award. He has also been awarded Fellowship of the Royal College of Surgeons of England ad eundum. He is an expert adviser to NICE Medical Technologies Evaluation Programme. Steve co-founded the Woundcare 4 Heroes charity, which is already making a big difference to the wound care of both serving and veteran personnel.
Dr Matthew Bayfield
Medical Specialist Scientific Director
Dr Matthew Bayfield, Head of Cardiothoracic Surgery, Strathfield Private Hospital and VMO Cardiothoracic Surgeon, Royal Prince Alfred Hospital.
Professor Peter Windsor
Veterinarian Research Advisor
Peter is a registered specialist veterinary surgeon in New South Wales and an emeritus Professor at Sydney University. He holds a BVSc (Hons), PhD, DVSc and diploma from the European College of Small Ruminant Health Management.
Dr Julian Braidwood
Global Regulatory Affairs Advisor
Julian has held leadership roles and managed international clinical projects with Grampian. He was previously Regulatory Affairs Manager at Novartis Animal Health. He is the Founder and Managing Director of Triveritas, where he is responsible for a team of 40 animal health specialists across the EU and the US.
Tri–Solfen®
Tri-Solfen® is a local anaesthetic and antiseptic gel spray that adheres well to wounds and acts as a barrier to environmental stimuli, promotes haemostasis and improves wound healing. Tri-Solfen® contains two proven topical local anaesthetics; fast-acting Lignocaine for immediate pain relief and long-acting bupivacaine for prolonged post-operative pain relief. Adrenaline is included for its ability to reduce the shock and stress of blood loss, whilst prolonging the anaesthetic action. Tri-Solfen® also contains Cetrimide; an antiseptic widely used to cleanse skin and wounds and provides protection from bacterial contamination.
About Medical Ethics
About humans
Chronic wound care
Medi-Solfen®
Supporting studies and references
Tri-Solfen®
Development and application
Products and pipeline
Scientific publications and references
Government and NGO support
News and videos
Medi-Solfen®– potential new pain mitigation technology for humans
Dr Matthew Bayfield, Medi-Solfen® researcher talks about the potential of this Medical Ethics product currently in development as a potential over-the-counter solution that could benefit a wide range of people; from parents to ambulance personnel and medics working in difficult locations such as battlefields.
Medi-Solfen® key points
Medi-Solfen®: A potential new topical analgesic for the reduction of pain when debriding Venous Leg Ulcers
Wounds result in a significant cost to the UK Healthcare system. It has recently been estimated the annual cost for treating wounds is £5 billion1 and this will rise significantly due to the increased proportion of elderly patients living longer. This figure represents 3% of the total healthcare spend. In terms of the community sector 60% of those wounds treated are chronic and the 3 major types seen are leg ulcers, diabetic foot ulcers and pressure ulcers. In the UK it is estimated that population prevalence rates generally fall in the range of 1.2–3.2 per 1,000 people.2 which means there are 70,000–190,000 individuals in the UK with a venous leg ulcer at any time. The cost to the NHS of treating patients with venous ulceration, mostly in primary care and through community nursing services, is at least £168–198m per year.3
The presence of dead or necrotic tissue (including slough) on the surface of any wound including venous leg ulcers will delay wound healing. Debridement which facilitates removal of such barriers to healing is an integral part of wound bed preparation and comprises the T (tissue removal) element in the TIME continuum to promote healing endorsed by most key opinion leaders and consensus groups4,5.
Patients with wounds often experience pain. However, there is evidence that this is often underestimated or mismanaged by health professionals6.
In addition, there are many psychological and emotional factors associated with living with a wound that can affect patients' perception of pain, such as anxiety, stress fear and depression7.
Sharp debridement of non-viable tissue is a frequent treatment modality for leg ulcer patients. However, the procedure is not well tolerated and patients will often ask the clinicians to stop before the debridement is completed because of the pain.8,9,10
It is possible that patients will deny future consent for the sharp debridement if the first experience was painful. This also impacts on the confidence of trained physicians to achieve the depth of tissue removal necessary for optimising the process of wound bed preparation. This poses difficulties in providing optimal care and in achieving healing in a timely manner. Delayed healing eventually creates additional costs and deterioration in the patient's quality of life. The UK NHS advocates a patient-centred approach, an approach that promotes physical comfort, including pain management11.
Current therapeutic options for wound pain relief during debridement include drug-based creams (EMLA cream) which take up to 1 hour to take effect prior to use of the scalpel8,10 and creates practical challenges in retention and possible re-application and hydrogels that may have to applied very frequently over weeks to achieve a clean wound bed12.
There is a clear need for an easy to apply product that will provide almost instantaneous and continuous pain relief prior to and after the debridement procedure. This will ensure increased confidence in achieving the wound bed preparation goals. From a patient perspective, whether it is their first time or an additional procedure, such benefits will remove any anxiety, fear or compliance with their treatment strategy. There is a clear fit with the NHS goals of achieving a patient-centred approach that promotes physical comfort, including pain management.13
From an economic perspective use of Medi-Solfen® has the potential to allow multiple debridement procedures to be routinely achieved at the start of any consultation which has the potential to result in faster healing14,15. Savings will be realised in terms of fewer nurse practitioner visits, dressing and retention bandages and in patient stays.
Lindholm C and Searle R (2016) Wound Management in the 21st Century Combining efficacy and effectiveness. Int Wound J; 13(Supp 2): 5-15. century:
Graham, I.D. et al (2003) Prevalence of lower-limb ulceration: a systematic review of prevalence studies. Advances in Skin and Wound Care; 16: 6, 305–316
Posnett J and Franks PJ (2008) The burden of chronic wounds in the UK. Nursing times; 104(3): 44-45
European Wound Management Association (EWMA) Position document. Wound Bed Preparation in Practice. London MEP Ltd 2004
Leaper DJ, Schultz G, Carville C et al. (2012)Extending the TIME concept. What we have learned in the last 10 years. Int Wound J; 9 (Supp 2): 1-19
Brown A. (2014) Strategies to reduce or eliminate wound pain. Nursing times; 110 (15): 13-15.
Vuolo JC (2009) Wound-related pain: key sources and triggers. Br J Nursing; 18(15): S20-S25.
Hansson, C., Holm, J., Stefan, L. and Syren, A. (1993) Repeated treatment with lidocaine/prilocaine cream (EMLA) as a topical anaesthetic for the cleansing of venous leg ulcers. Acta Dermato-Venereologica. 73: 231–233.
Enander Malmros I, Nilsen T, Lillieborg S. (1990) Plasma concentrations and analgesic effect of EMLA (Lidocaine/Prilocaine) cream for the cleansing of leg ulcers. Acta Dermato-Venereologica. 70(3): 227–30.
Lok, C. et al (1999) EMLA cream as a topical aesthetic for the repeated mechanical debridement of venous leg ulcers: a double-blind, placebo-controlled study. Journal of the American Academy of Dermatology. Volume 40, issue 2, pp. 208- 213.
NHS Paper summarising Patient experience Framework (2011). Gateway reference 17273.
Edwards H, Gibb M, Finlayson K, Jensen R. (2013) Champions for Skin Integrity Wound Dressing Guide. Hydrogels p16-19. Brisbane : Queensland University of Technology. E: woundservice@qut.edu.au ISBN 978-1-921897-79-5
Steed DL, Donohoe D, Webster MW, Lindsley L (1996) Diabetic Ulcer Study Group. Effect of extensive debridement and treatment on the healing of diabetic foot ulcers. J AmColl Surg; 183(1): 61-64.
Wilcox JR, Carter MA and Covinton S (2013) Frequencies of debridement and time to heal. A retrospective cohort study of 312744 wounds. JAMA Dermatol; 149(9): 1050-1058.
Medi-Solfen® technology has the potential to deliver a rapid onset
Surgical debridement uses sharp instruments (such as a scalpel, scissors and other sharp instruments) to remove necrotic tissue from the wound bed, either at the patient's bedside or in specialised clinics. The advantages of such approaches include excellent control over the selection of tissue type to be removed and how much tissue to remove. It is the fastest way to achieve a clean wound bed and an increased frequency of debridement of this kind has the potential to speed up the healing process1,2 which presents clinical, patient and economic advantages. A major disadvantage is that the use of sharp instruments may be painful for the patient. The pain type is described as procedural/operative pain which by definition causes pain that results from routine procedures such as dressing changes or wound cleansing, or is associated with significant wound interventions, such as biopsies or debridement3. Rapid control of such pain will impact on the patient's overall experience of the procedure and also improve subsequent compliance to attend future events of this nature and adhere to dressing changes. It is possible that patients will deny future consent for the sharp debridement if the first experience was painful. This poses difficulties in providing optimal care and in achieving healing in a timely manner. Delayed healing eventually creates additional costs and deterioration in the patient's quality of life. Some anaesthetic containing creams such as EMLA can take up to 1 hour post application to attain sufficient levels of anaesthesia to allow the debridement process to commence. This extends considerably the procedure duration times, levels of anticipation surrounding what the patient may be expecting to happen (especially if pain has been encountered in previous visits) and affect resource utilisation strategies within the clinical facility. With the increasing number of venous ulcers being treated questions can be raised about the ability of healthcare professionals to meet, for example, CQUIN wound care goals with the additional timings required for routine but essential procedures such as debridement4.
Having access to a proven, rapid onset, multimodal anaesthetic gel with additional bacterial agents and adrenaline such as Medi-Solfen® allows faster turnaround times for debridement procedures within any clinic situation. This will positively impact on clinical resource utilisation initiatives increasing productivity. The rapid onset of effective anaesthesia also offers great benefits to the patient, avoiding previous negative experiences associated with pain and making the overall experience more accommodating to enhance overall compliance with treatment. This also aligns itself to the UK NHS advocating a patient- centred approach, an approach that promotes physical comfort, including pain management5.
Wilcox JR, Carter MA and Covinton S (2013) Frequencies of debridement and time to heal. A retrospective cohort study of 312744 wounds. JAMA Dermatol; 149(9): 1050- 1058.
Commissioning for Quality and Innovation (CQUIN). Guidance for 2017-2019 Publications Gateway Reference 06023. Nov 2016
Medi-Solfen®, a topical analgesic, has the potential for use during pre-closure of surgical wounds in a multi-modal approach to post-surgical pain mitigation
In 2013/2014 there were 4.7 surgical admissions in England which represents a 27% increase since 2003/2004. Specialists with the highest activity include general surgery 1.3m, trauma/orthopaedics 1.2m and urology 736,000. The most common procedures were hernia repair (all forms) 120,000, hip replacement 116,000, knee replacement 82,000, gall bladder removal 76,000 and tonsillectomy 51,000. Emergency laparotomies are estimated to be 30,000-50,000 per annum1. According to the latest data from the National Centre for Health Statistics, 48 million surgical inpatient procedures were performed in the United States in 20092.
Post-operative acute pain management is a major health issue and is costly to the health care system3. Pain contributes to poor quality of life, reduced well-being, physical disability and mortality4. One source of pain includes surgical procedures.
Unrelieved postsurgical pain is common and may be a useful context in which to study pain- related morbidity and mortality. For example, postoperative pain in hip fracture patients predicted longer hospital length of stay (LOS), delayed ambulation and long-term functional impairment5. Local anaesthetic (LA) infiltration prior to surgical incision closure is a frequently used technique in the operating room. The technique of injecting local anaesthetics into the various layers of the surgical incision (wound) is also a commonly used practice in general anaesthesia surgical cases6. Surgical wound infiltration with local anaesthetics has continued to increase in popularity since the mid 1990's7. It is relatively inexpensive, technically not difficult and may potentially reduce the post-operative discomfort7.
Even though pain results from complex physiologic mechanisms that involve multiple receptors in both the central and peripheral nervous systems, single or monotherapy with opioids has been a foundation of postsurgical pain management. However, no single analgesic targets all types of pain receptors or signalling pathways; furthermore, the amount of opioids that can be administered is limited due to the risk for adverse drug events that lead to patient discomfort, delayed recovery, prolonged LOS, and increased costs8.
The use of multimodal analgesia involves the administration of two or more analgesic agents that act through different mechanisms with the goal of improving postsurgical pain management.
Non-opioid alternatives, e.g. NSAIDs, acetaminophen, and local anaesthetics are recognized as effective components of a multimodal pain regimen postoperatively. A multimodal approach can reduce opioid use and opioid-related adverse drug events and also result in earlier patient ambulation as well as discharge. Professional guidelines endorse the use of multimodal therapies which should be individualised for the particular patient, operation and circumstances. Understanding of both the range of available interventions and considering the type of surgical procedure are essential to safe and effective pain management. (Veterans Administration/Department of Defence (VA/DoD) Clinical Practice Guideline for the Management of Postoperative Pain). The guidelines also state that the selection of a pain management option should be determined by balancing the advantages, disadvantages, contraindications, as well as patient preference. For most patients, more than one modality will be needed for successful pain management.
Examples of local anaesthetics that are commonly infiltrated include moderate duration agents such as lidocaine, Mepivacaine and Prilocaine and long duration agents such as Bupivacaine and Etidocaine9. Local infiltration may however cause a haematoma to form if the needle damages a blood vessel. Other methods include use of a catheter to infuse local anaesthetic post operatively. This can be done through a catheter laid directly in the wound, or by a catheter placed in a key nerve region nearby (such as a paravertebral catheter placed at thoracotomy to block intercostal nerves at multiple levels). The catheter may stay 2 or 3 days after surgery. There are potential risks with this which include failure of the catheter to sit in the right spot and therefore be ineffective at delivering the local anaesthetic to the regional nerves, risk of infection tracking along the catheter track, or even the catheter being inadvertently retained by a wound closure suture passing through it (meaning re-operation to release the catheter).
Medi-Solfen® could provide a unique innovative approach to anaesthesia prior to surgical closure
Medi-Solfen® offers the surgeon a product that contains all of the components of multimodal therapy in one very simple to apply gel negating the need for individual injections associated with multimodal anaesthetic therapy. Medi-Solfen® is a sterile, cutaneous gel containing four well established active ingredients; lidocaine hydrochloride 5%w/w (equivalent to 4% lidocaine), 0.5%w/w bupivacaine hydrochloride, 0.00451%w/w adrenaline acid tartrate and 0.5%w/w cetrimide in a fixed combination product. As the active ingredients are well- established as local anaesthetics (lidocaine and bupivacaine), as a vasoconstrictor (adrenaline) and as an antiseptic (cetrimide) it offers a unique combination of ingredients not found together in any other product. Use of an agent like Medi-Solfen® can avoid the complications previously highlighted associated with the use of needles. These include no risk of haematoma from use of a needle for infiltration, no swelling of tissues from the volume of local anaesthetic injected around the wound, no catheter to need precise placement or to act as a hazardous foreign body. Additionally the application of Medi-Solfen® directly in onto the wound during closure may act as a "depot" for continued release of the local anaesthetic from the gel for a few hours afterwards.
https://www.rcseng.ac.uk/news-and-events/media-centre/media-background- briefings-and-statistics/surgery-and-the-nhs-in-numbers/
https://stanfordhealthcare.org/medical-clinics/surgery-clinic/patient-resources/surgery-statistics.html
Allegri M, Clark MR, De Andres J, et al. (2012) Acute and chronic pain: where we are and where we have to go. Minerva Anestesiol; 78: 222-235.
McGuire L, Heffner K, Glaser R et al. (2006). Pain and wound healing in surgical patients. Ann Behav Med;
31(2): 165-172.
Morrison, RS, Magaziner J, McLaughlin et al. (2003) The impact of post-operative pain on outcomes following hip fracture. Pain; 103: 303-311.
Scott NB (2010) Wound infiltration for surgery. Anaesthesia 65 Suppl 1: 67-75.
Johnson RC, Hedges AR, Morris R, Stamatakis JD (1999) Ideal pain relief following laparoscopic cholecystectomy. Int J Clin Pract 53: 16-18.
Moss Rose (2015) Infiltration of local anaesthetics for Postoperative analgesia. Ongoing Education Initiative Pfeidler Enterprises.
Surgeon's Guide to Postsurgical Pain Management: Colorectal and Abdominal Surgery, 1st ed. West Islip, NY: Professional Communications, Inc.; 201.)
Reducing pain associated with VLU debridement has the potential to indirectly improve healing rates as the more aggressive the debridement the faster the wound will heal
Wounds heal faster when debrided often by trained healthcare professionals. Published studies have shown that faster and more complete healing was achieved with more frequent debridement regardless of wound type, size or duration1,2. Weekly or even more frequent debridement resulted in shorter healing times compared with less frequent debridement. Education and training for proper debridement practices should not be limited to physicians but should include general staff members in order to make the flow of wound care more efficient. Nearly twice as many Venous Leg Ulcer's and Diabetic Foot Ulcer's healed completely with frequent debridement compared with those treated less frequently (50% v 28%).
The clinical professional has a range of options to achieve debridement and choice will depend on the pain threshold of the patient, type of necrotic tissue and where the patient is being treated. The fastest debridement procedure is sharp debridement usually associated with the use of a scalpel or similar instrument. The gentler approach such as the use of hydrogels may take weeks and many visits to facilitate dressing changes and re-application of the hydrogel and is costly and time consuming. Patients who undergo sharp debridement may feel greater pain than other approaches and this may impact on their compliance to undergo the necessary number of debridements to achieve an optimal wound bed that can start to progress towards healing. Also due to the level of procedural pain they may ask an immediate cessation of treatment at any stage during the process.
The need exists for not only a rapid approach to achieving pain relief immediately before the debridement procedure, but also the provision of sustained pain relief for some hours after completion. Research suggests that Medi-Solfen® offers these benefits and would provide increased compliance to achieve completion of the procedure and an increased willingness to return for future visits if required. The impact on the patient's quality of life will be heightened if the stalled wound can be moved to an increased trajectory of healing faster. From a clinical perspective sharp debridement in pain free circumstances allows faster and more accurate removal of the appropriate amounts of dead tissue without interference from the patient asking to stop due to unbearable pain levels. Other pharmaceutical approaches to wound pain management can take up to 1 hour to attain the necessary level of anaesthesia prior to surgical intervention which adds to anxiety and stress for the patient anticipating what is coming next!
Steed DL, Donohoe D, WebsterMW, Lindsley L (1996) Diabetic Ulcer Study Group. Effect of extensive debridement and treatment on the healing of diabetic foot ulcers. J AmColl Surg; 183(1): 61-64.
Medi-Solfen® also has the potential to improve patient quality of life
Patients with chronic leg ulcers describe their experience as challenging and difficult. Patients experience their body as unreliable, which in their daily life means that it may be a source of social embarrassment – and possibly eventual isolation due to symptoms such as bad smell, excess of exudate, and pain.1
There are several types of wound pain but of relevance to the use of Medi-Solfen® is the pain type described as "procedural/operative" which is pain that results from routine procedures such as dressing changes or wound cleansing, or is associated with significant wound interventions, such as biopsies or sharp debridement. Sharp debridement of non-viable tissue is a frequent treatment modality for leg ulcers patients. However, the procedure is not well tolerated and patients will often ask the clinicians to stop before the debridement is completed because of the pain2,3,4
It is possible that patients will deny future consent for the sharp debridement if the first experience was painful. This poses difficulties in providing optimal care and in achieving healing in a timely manner. Delayed healing eventually creates additional costs and deterioration in the patient's quality of life. Debridement procedures are painful not only during the procedure but hours and days after the procedure as well.
The NHS aims at providing patients with a positive experience of the health system, of physical comfort and advocates emotional support and alleviation of fear and anxiety about such issues as clinical status and its treatment5. In this perspective one could say that management of pain is a marker of the quality of care and a way of improving people's when the wound did not hurt. When patients felt an ease or absence of pain they interpreted it as a positive sign of wound healing, which made them feel hopeful and optimistic6. Pain measurement within the holistic process of quantifying impact on a patient's quality of life could and probably will become a key goal for future initiatives.
Bland, M. (1999) On living with chronic leg ulcers. In Nursing and the Experience of Illness: Phenomenology Practice. Editors: Irena Madjar and Jo Ann Walton. Publishers: Allen & Unwin, pp. 36-56.
Lok, C. et al (1999) EMLA cream as a topical anaesthetic for the repeated mechanical debridement of venous leg ulcers: a double-blind, placebo-controlled study. Journal of the American Academy of Dermatology. Volume 40, issue 2, pp. 208-213.
Goldberg, E. and Beitz, J. (2010) The Lived Experience of Diverse Elders With Chronic Wounds. Ostomy Wound Management. Volume 56, issue 11, pp. 36-46.
Medi-Solfen® has the potential to offer a unique innovative approach to providing anaesthesia within the Accident and Emergency environment including the Ambulance Service
In the UK there are 135 emergency units1. Within England the number of attendances in 2016 was 23.7m2 (65% attending Major Emergency Departments). In 2001, the Department of Health published the paper Reforming emergency care3 and introduced a compulsory national target for England. The target required that by 2004 no-one should wait more than 4 hours in the Emergency Department. In December 2017 just 85.1% of patients at A&E were seen within 4 hours. The figures are even worse for what the NHS calls Type 1 A&E Departments – a Consultant led 24 hour service with full resuscitation facilities and designated accommodation for emergency patients – where just 77.3 per cent of patients were seen within 4 hours4. This time limit produced significant changes in the way many departments and hospitals dealt with their workload in the Emergency Department, and included many initiatives to reduce the total time and redirect patients with low acuity to alternative healthcare providers. One of the most noteworthy changes was the review of the process of "triage" and the change of the primary objective of triage—to allocate the patient to the most appropriate practitioner or area within the healthcare system, thus producing different streams or queues of patients waiting for dedicated teams of workers5.
Emergency care providers have developed a high level of expertise in acute wound management. As an example over 703,000 lacerations presented in UK Emergency Departments between 2015 In the case of this wound type considerations must be given to assessment, irrigation and closure techniques. No single approach can be applied to all wounds; however, a systematic approach to acute wound care integrated with current best practices can provide the framework for exceptional wound management. During the treatment pathway associated with laceration management it may be necessary to administer local anaesthetics to the injured site. While there are numerous commercially available topical anaesthetic agents, most of these require 10 to 30 min to become effective. The combination of lidocaine/prilocaine may have a delayed onset of 1 to 2 h ]. If a more rapid anaesthetic response is needed, injectable lidocaine (1%), bupivicaine (0.25%), or procaine (1%) are commonly used. While these drugs remain the mainstay of anaesthesia for cutaneous repair, the associated pain on injection remains a major drawback6.
Of relevance to the benefits associated with the use of Medi-Solfen®, rapid pain relief following application to traumatic wounds at initial triage and assessment would help patients better manage their extended wait periods before consultation with Lead Clinical Professionals. Once in the presence of the attending Physician, the rapid onset of additional anaesthesia (if required) without using the potential painful technique of fluid injection prior to debridement, irrigation and subsequent closure again offers measureable patient benefits. The product could also be re-applied prior to surgical closure if considered clinically necessary. The same approach could be made with minor painful wounds that present, especially in children.
An essential component of the Emergency Services is the rapid response vehicles (ambulances) that transfer patients from the site of injury to the Accident and Emergency Department. It is estimated in the UK there are close to 5,000 vehicles of this kind. This does not include Emergency Responders or the Air Ambulance Service. The inclusion of Medi-Solfen® within emergency vehicles could provide a valuable option to achieve rapid pain relief to appropriate breaks in the skin during treatment at the site of injury, transfer to hospital and provide anaesthetic cover during the reported ever increasing wait times prior to hand over to the hospital-based team.
https://inews.co.uk/nhs/nhs-crisis-revealed-overhaul-means-dozens-of-ae-units- face-closure/
Baker C. House of commons library paper 6964, 21st Feb 2017. Accident and Emergency Statistics Demand, Performance and Pressure
Department of Health Reforming emergency care: first steps to a new approach. Crown Copyright. London: DOH, 2001
https://inews.co.uk/news/health/accident-emergency-waiting-times-nhs-england- record-high/
Lyons M, Brown R and Wears R (2007) Factors that affect the flow of patients through Triage. Emerg Med J; 24(20): 78-85.
Bret A, Ayello E, Woo K et al (2010) Acute wound management; Revisiting the approach to the assessment, irrigation and closure considerations.
Medi-Solfen® has the potential to have a major role in military and mass casualty trauma situations
The recent wars in Iraq and Afghanistan have helped to shape the modern Defence Medical Services. Over the course of these conflicts there were a number of incremental innovations and improvements in clinical techniques and attitudes that contributed to the overall effect of reducing the mortality from combat injury. Significant resources were allocated to prepare for and deliver a coherent plan for deployed trauma care. The medical advances during the recent conflicts in these parts of the world have also included advances in anaesthesia and analgesia, but to a lesser extent than in other areas. The priority has so far been on improving survival rates. The humanitarian and physiological consequences of analgesia have featured less highly on the priority list.
Presently, with the level of small arms and fragment protection that is issued to Armed Forces, the survival rate following combat trauma is approximately 98%; however, there has been an increase in the number of extremity, groin, and facial wounds, as these are areas that are not as well shielded by individual combat armour1. Many of the concerns and obstacles faced by early anaesthesia providers continue to exist today. The needs for safety, rapid application to surface injuries, mobility and availability of logistical resupply are all concerns for military anaesthesia providers.
The ideal analgesic for military use should have a predictable action, no side effects, a long duration of action, a readily available antidote, be easily administered and be easily stored and transported2.
A Combat Medic will typically carry a backpack styled bag known as a "Unit One Pack". Aid bags are available from many different manufacturers, in many different styles. Depending on the unit and their standard operating procedures, the Medic may have to follow a strict packing list, or may have the liberty of choosing their kit depending on the mission at hand. In terms of analgesics a typical aid bag will include: Morphine, Naproxen and some OTC products such as Acetaminophen and Ibuprofen3. Depending on the injury pain control may involve a combination of simple measures and different drugs. Morphine auto-injectors are issued to many countries' armed forces on operations. All UK soldiers receive ample training on the use of the morphine auto-injector. Confidence in using the device is high and generally knowledge is good4. Unwanted side effects associated with Morphine use include respiratory depression, constipation and constriction of the pupils of the eye all of which may affect overall performance in combat situations. The goal in a casualty with mild-to- moderate pain is to provide pain relief that does not affect their sensorium. This allows them to either continue to facilitate their mission set or to help facilitate their own medical care and evacuation, depending on circumstances. In the wilderness setting, this would, in particular, apply to the casualties being able to facilitate their own evacuation5. The respiratory depression that is associated with opiate administration may result in the casualty requiring airway support, greatly complicating any movement.
Wound infection following combat injury is a cause of significant morbidity and occasional mortality6. Combat injury is often filthy, with ingrained dirt containing many troublesome microbes, both bacterial and fungal. These sow the seed for problems which may continue for many years after the injury7. Currently there is no provision for the delivery of any topical antimicrobial agents prior to the arrival of the patient at the Field Hospital.
Now that the survival rate has significantly improved following combat injury, perhaps now is the time to concentrate more effort into the humanitarian and other physiological effects of better anaesthesia, as well as ways of reducing the wound infection rate.
Medi-Solfen® offers the potential for a safe, effective replacement for Morphine that can both be easily and quickly applied and have immediate effect. It is important that delivery of these multi-modal anaesthetics has minimal psychoactive effects so that patients can continue to assist in their own care, evacuation and defence. An additional major benefit offered is that these drugs would act only at the wound site and not systemically. The inclusion of adrenaline into the overall formulation could also have a beneficial effect in controlling surface bleeding. Compared with opiates, which are Controlled Substances and Accountable Items, it would be relatively easy to envisage every soldier carrying an application of Medi-Solfen® in his first aid kit. Cost is also a factor in what medications are carried and utilized. Generic non-prescription medications such as Acetaminophen and Ibuprofen are available at minimal cost, whereas morphine injectors are much more expensive. There is also much less potential for criminal abuse of an item such as Medi-Solfen, unlike opiates. The logistics of the issuing of Medi-Solfen should therefore be much less onerous. The individual provider will need to decide which analgesics he or she should carry based on cost as well as regulatory and standard care pathway considerations.
In addition to military conflicts disaster situations, such as earthquakes, floods, conflicts, might happen in areas where access to a regular hospital or treatment centres might be hours away or not available at all. The provision of effective analgesia for mass casualties needs to be simple in its scope and application, supporting the principle of providing the greatest good for the greatest number in the safest way. The care of wounded victims, and the building or rebuilding of medical and first-aid facilities falls to the role of humanitarian assistance and disaster relief agencies such as the United Nations, Medecins Sans Frontieres and the IRC. These agencies are funded by donations and/or government funding and grants. Similar to the military, all of these agencies source and supply basic medical necessities to their Field Officers for the management of wounded victims and for the setting up of basic medical facilities. A product like Medi-Solfen® has the potential to become a critical component of the basic medicines supplied. It is ideally suited to such applications because it is cheap, portable and able to be applied immediately by rapidly trained lay personnel. It would provide a means of promptly treating wounds that otherwise may remain untended for prolonged periods of time particularly in war-torn or third-world countries. Indeed in many cases such wounds may not receive any other anaesthetic. The monitoring of such casualties may need to rely on minimally trained personnel using simple clinical parameters. When casualties present in large numbers with minor injuries resulting in breakdown of the skin Medi-Solfen can provide an effective rapid solution to pain relief during potential long waits for initial triage or allow casualties to return for later treatment if not in imminent danger. The benefits of having a cheap, simple to use product to relieve pain, minimise bleeding and protect against infection in these circumstances are considerable. Medi-Solfen® has the potential to act as the 'front line' pain relief for topical wound care product for victims of trauma throughout the world.
Jeffery SLA. Advanced wound therapies in the management of severe military lower limb trauma: a new perspective. Eplasty 2009; 21: e28
Battlefield Advanced Training Life Support. Chapter 14 Analgesia. JR Army Med Corps (2003); 149: 297-302
Equipment of a combat medic https://www.google.co.uk/search?q=morphine+in+soldiers+combat+back+packs&rlz
=1C1GCEA_enGB784GB784&oq=morphine&aqs=chrome.1.69i57j35i39j0l4.5917j0j8 &sourceid=chrome&ie=UTF-8
Nelson SC and Wedgwood JT (2015.) How much do soldiers know about the morphine they carry on operations? A questionnaire study of knowledge and understanding of the morphine auto-injector on Op HERRICK 17. J R Army Corps; 161(1): 27-31
Wedmore IS and Butler FK Jr (2017) Battlefield analgesia in Tactical Combat Casualty Care. Wilderness and Environmental medicine;28: S109-S116
Taylor C, Jeffery SLA. Management of military wounds in the modern era. Wounds UK 2009; 5: 50-58.
Jeffery SL. The Management of Combat Wounds: The British Military Experience. Adv Wound Care 2016 Oct 1; 5(10): 464-473.
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The medal marked service in the short war of 1939 between Japan and the Soviet Union on the border of the Japanese puppet state of Manchuko. There are two known variations of this medal, this being the type designated as "Variant 1", with a thinner dove on the obverse. Excellent condition.


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text:
\section{Introduction}
\label{}

Computing the average $\mu(\varphi)=\int_{\mathcal{D}}\varphi(x)\mu(dx)$ of a function $\varphi:\mathcal{D}\to \mathbb{R}$, with respect to a probability distribution $\mu$ defined on $\mathcal{D}\subset \mathbb{R}^d$, is typically a challenging task in many applications (e.g. chemistry, statistical physics, see e.g.~\cite{LeimkuhlerMatthews}), since usually $d$ is large and $\mu$ is multimodal.

In the sequel, we assume that $\mathcal{D}=\mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d$ is the flat $d$-dimensional torus, and that $\mu$ writes
\begin{equation}\label{eq:mu_simple}
\mu(dx)=\mu_\beta(dx)=\frac{\exp\bigl(-\beta V(x)\bigr)}{Z(\beta)}dx,
\end{equation}
where $V:\mathbb{T}^d\to \mathbb{R}$ is a smooth potential function, $\beta\in(0,+\infty)$ is the inverse temperature, $dx$ denotes the Lebesgue measure on $\mathbb{T}^d$ and $Z(\beta)$ is a normalizing constant.
In this context, the multimodality of $\mu_{\beta}$ follows, in the case of so-called energetic barriers, from the existence of several local minima of $V$.

A standard approach to computing $\mu_\beta(\varphi)$ is to consider the following SDE on $\mathbb{T}^d$ (overdamped Langevin dynamics):
\begin{equation}\label{eq:OL_simple}
dX_t^0=-\nabla V(X_t^0)dt+\sqrt{2\beta^{-1}}dW_t, \quad X_0^0=x.
\end{equation}
where $\bigl(W(t)\bigr)_{t\ge 0}$ is standard Brownian Motion on $\mathbb{T}^d$. Indeed, it is well-known that, for any continuous function $\varphi:\mathbb{T}^d\to \mathbb{R}$ almost surely
\begin{equation}\label{eq:ergo_simple}
\frac{1}{t}\int_{0}^{t}\varphi(X_r^0)dr\underset{t\to +\infty}\to \int_{\mathbb{T}^d}\varphi(x)\mu_\beta(dx),
\end{equation}
However, this convergence may be very slow, when $\beta$ is large and $V$ has several minima: the stochastic process $X^0$ is then metastable, and hopping from the neighborhood of one local minimum of $V$ to another is a rare event which may have a strong influence on the estimation of averages $\mu_\beta(\varphi)$

Many strategies based on importance sampling techniques --  self-healing umbrella-sampling \cite{marsili2006self}, well-tempered metadynamics \cite{barducci2008well}, Wang-Landau algorithms, adaptive biasing force, etc... -- have been proposed and applied to improve the convergence to equilibrium of stochastic processes in order to compute approximations of $\mu_{\beta}$. We refer for instance to~\cite{LelievreRoussetStoltz:10} and references therein for a mathematical review.

In this work, we focus on an Adaptive Biasing Potential (ABP) method, given by the system~\eqref{eq:ABP_simple}. The method was designed in~\cite{DicksonLegollLelievreStoltzFleurat:10,marsili2006self} for problems in chemistry, and up to our knowledge no rigorous general mathematical analysis has been performed so far. Precisely, in~\eqref{eq:OL_simple}, $V$ is replaced with a time-dependent and random potential function $V_t$ which is modified adaptively, using the history of the process up to time~$t$: $A_t$ depends on the values of the associated stochastic process $X_r$ for all $0\le r\le t$. Here, $V_t=V-A_t\circ\xi$, where, for some $m\in\left\{1,\ldots,d-1\right\}$, $A_t:\mathbb{T}^m\to \mathbb{R}$ and $\xi:\mathbb{T}^d\to \mathbb{T}^{m}$ is a smooth function,  referred to as the {\it reaction coordinate} mapping. In applications, usually $m\in\left\{1,2,3\right\}$. To simplify further the presentation, we assume that $\xi(x_1,\ldots,x_d)=(x_1,\ldots,x_{m})$; in this case, $z=(x_1,\ldots,x_{m})=\xi(x_1,\ldots,x_d)$ (resp. $z^\perp=(x_{m+1},\ldots,x_d)$) is interpreted as the slow (resp. fast) variable.

The dynamics of the ABP method is given by the following system
\begin{equation}\label{eq:ABP_simple}
\begin{cases}
dX_t=-\nabla\bigl(V-A_t\circ \xi\bigr)(X_t)dt+\sqrt{2\beta^{-1}}dW(t)\\
\overline{\mu}_t=\frac{\overline{\mu}_0+\int_{0}^{t}\exp\bigl(-\beta A_r\circ\xi(X_r)\bigr)\delta_{X_r}dr}{1+\int_{0}^{t}\exp\bigl(-\beta A_r\circ\xi(X_r)\bigr)dr}\\
\exp\bigl(-\beta A_t(z)\bigr)=\int_{\mathbb{T}^d}K\bigl(z,\xi(x)\bigr)\overline{\mu}_t(dx),~\forall z\in\mathbb{T}^m,
\end{cases}
\end{equation}
where a smooth {\it kernel} function $K:\mathbb{T}^m\times \mathbb{T}^m \to (0,+\infty)$, which is such that $\int_{\mathbb{T}^m}K(z,\zeta)dz=1, \forall \zeta\in \mathbb{T}^m$, is introduced to define a smooth function $A_t$ from the distribution $\overline{\mu}_t$. The unknows in~\eqref{eq:ABP_simple} are the stochastic processes $t\mapsto X_t \in\mathbb{T}^d$, $t\mapsto \overline{\mu}_t\in \mathcal{P}(\mathbb{T}^d)$ (the set of Borel probability distributions on $\mathbb{T}^d$, endowed with the usual topology of weak convergence of probability distributions), and $t\mapsto A_t\in \mathcal{C}^{\infty}(\mathbb{T}^m)$ (the set of infinitely differentiable functions on $\mathbb{T}^m$). In addition to~\eqref{eq:ABP_simple}, arbitrary (and deterministic, for simplicity) initial conditions $X_{t=0}=x$, $\overline{\mu}_{t=0}=\overline{\mu}_0$ and $A_{t=0}=A_0$ are prescribed.

The third equation in~\eqref{eq:ABP_simple} introduces a coupling between the evolutions of the diffusion $X_t$ and of the {\it weighted empirical distribution} $\overline{\mu}_t$: then $X$ can be seen as a self-interacting diffusion process, like in~\cite{BenaimLedouxRaimond1}.

Our main result is the consistency of the ABP approach.
\begin{theorem}\label{th:cv_mu}
Almost surely, $\overline{\mu}_t\underset{t\to +\infty}\to\mu_{\beta}$, in $\mathcal{P}(\mathbb{T}^d)$.
\end{theorem}

With standard arguments, Theorem~\ref{th:cv_mu} yields almost sure convergence of $A_t$ in $\mathcal{C}^{k}(\mathbb{T}^m)$, for all $k\in\mathbb{N}$.
\begin{corollary}\label{cor:cv_A}
Set $\exp\bigl(-\beta A_\infty\bigr)=\int K(\cdot,\xi(x))\mu_{\beta}(dx)$. Then almost surely, $A_t\underset{t\to +\infty}\to A_\infty$, in $\mathcal{C}^{k}(\mathbb{T}^m)$, $\forall~k\in\mathbb{N}$.
\end{corollary}

The limit $A_\infty$ is an approximation of the function known as the {\it free energy} $A_\star$ (see~\eqref{eq:A_simple}), which depends on $V$, $\beta$ and $\xi$. As explained in Section~\ref{sec:FE}, the construction of the adaptive dynamics~\eqref{eq:ABP_simple} is motivated by an efficient non-adaptive biasing method, \eqref{eq:bias_simple}, which depends on $A_\star$. Computing $A_\star$ is the aim of many algorithms in molecular dynamics (see~\cite{LelievreRoussetStoltz:10}), and adaptive methods are among the most used in practice. Our result, Theorem~\ref{th:cv_mu}, answers positively the important question of the consistency of ABP method.

The remaining part of the article is organized as follows. In Section~\ref{sec:FE}, we define the free energy function $A_\star$, and explain why non-adaptive and adaptive biaising methods which are related to this function are interesting in the context of metastable dynamics~\eqref{eq:OL_simple}. In Section~\ref{sec:ABP}, we detail the strategy for the proof of Theorem~\ref{th:cv_mu}: we prove a stability estimate for $A_t$, and then introduce a random change of variables, based on a change of time. We are then in position to adapt the strategy of proof from~\cite{BenaimLedouxRaimond1} in our setting, which is based on the ODE method from stochastic approximation. The main essential role of the change of variables is the identification of the limit flow

The main result Theorem~\ref{th:cv_mu} holds in a more general setting, with appropriate modifications, than that of the present paper. For instance, the overdamped Langevin dynamics may be defined on the non-compact space $\mathbb{R}^d$ instead of $\mathbb{T}^d$; one can also consider the (hypoelliptic) Langevin dynamics, or infinite-dimensional dynamics (parabolic SPDEs). It is also possible to study the efficiency of the method in terms of a Central Limit Theorem. These generalizations will be studied in~\cite{BenaimBrehier}.

\section{Free energy and construction of the ABP dynamics~\eqref{eq:ABP_simple}}\label{sec:FE}

The aims of this section are to explain first how the ABP method~\eqref{eq:ABP_simple}, is constructed in a consistent way (the limit in Theorem~\ref{th:cv_mu} is $\mu_\beta$); and second why it is expected to be efficient (a rigorous analysis of the efficiency is out of the scope of this work).

Observe that $\exp\bigl(-\beta A_\infty(z)\bigr)=\int_{\mathbb{T}^m}K(z,\zeta)\exp\bigl(-\beta A_{\star}(\zeta,\beta)\bigr)d\zeta$, where $A_\star(\cdot,\beta)$ is the free energy (at temperature $\beta^{-1}$), defined by: for all $z\in \mathbb{T}^m$
\begin{equation}\label{eq:A_simple}
\exp\bigl(-\beta A_{\star}(z,\beta)\bigr)=\int_{\mathbb{T}^{d-m}}\frac{\exp\bigl(-\beta V(z,z^\perp)\bigr)}{Z(\beta)}dz^\perp.
\end{equation}
Usually, $K(z,\zeta)=K^\epsilon(z,\zeta)=\frac{1}{\epsilon}\tilde{K}\bigl((\zeta-z)/\epsilon\bigr)$, where $\epsilon\in(0,1)$ and $\tilde{K}:\mathbb{R}^m\to (0,+\infty)$ is symmetric, smooth, with compact support in $[-1/2,1/2]$; then $A_\infty^\epsilon$ converges to $A_\star(\cdot,\beta)$, in $\mathcal{C}^\infty$. Choosing $\epsilon$ sufficiently small, $A_t$ almost surely approximates the free energy $A_{\star}(\cdot,\beta)$ when  $t\to +\infty$, thanks to Corollary~\ref{cor:cv_A}.

Equation~\eqref{eq:A_simple} means that $\exp\bigl(-\beta A_{\star}(z,\beta)\bigr)dz\in \mathcal{P}(\mathbb{T}^m)$ is the image $\mu_\beta\bigl(\xi^{-1}(\cdot)\bigr)$ of $\mu_\beta$ by $\xi$. The free energy gives an effective potential along $\xi$, which is chosen in practice such that $\bigl(\xi(X_t^0)\bigr)_{t\ge 0}$ is metastable; this is related to $\mu_\beta\bigl(\xi^{-1}(\cdot)\bigr)$ being metastable, for instance when $A_{\star}(\cdot,\beta)$ has several local minima.

This is why in many applications, computing free energy differences $A_{\star}(z_1,\beta)-A_\star(z_2,\beta)$ is essential, see~\cite{LelievreRoussetStoltz:10}. The free energy function also theoretically provides efficient importance sampling algorithms; however these algorithms can only be implemented if $A_\star$ is explicitly known, and adaptive strategies allow to circumvent this practical difficulty.  Define biased probability distribution and dynamics
\begin{equation}\label{eq:bias_simple}
\begin{gathered}
\mu_{\beta}^{{\star}}=\frac{\exp\bigl(-\beta\bigl[V(x)-A_{\star}(\xi(x),\beta)\bigr]\bigr)}{Z(\beta)}dx\\
dX_{t}^{\star}=-\nabla\bigl[V-A_{\star}(\xi(\cdot),\beta)\bigr](X_{t}^{\star})dt+\sqrt{2\beta^{-1}}dW(t),
\end{gathered}
\end{equation}
by replacing the original potential function $V$ with the biased potential function $V-A_{\star}\bigl(\xi(\cdot),\beta\bigr)$ in~\eqref{eq:mu_simple} and~\eqref{eq:OL_simple}. Note that $\mu_{\beta}^{\star}$ is the unique invariant distribution of $X^\star$. By construction, it is easy to check that the image by $\xi$ of $\mu_{\beta}^{\star}$ is the uniform distribution $dz$ on $\mathbb{T}^m$, {\it i.e.} the associated free energy is equal to $0$.

Now define (unweighted) empirical distributions associated with~\eqref{eq:OL_simple} and~\eqref{eq:bias_simple}  respectively:
$$\rho_t^0=\frac{1}{t}\int_{0}^{t}\delta_{X_r^0}dr \quad,\quad \rho_t^\star=\frac{1}{t}\int_{0}^{t}\delta_{X_r^\star}dr.$
Then, by~\eqref{eq:ergo_simple}, the image by $\xi$ of $\rho_t^0$, resp. $\rho_t^{\star}$, converges almost surely in $\mathcal{P}(\mathbb{T}^m)$, to $\exp\bigl(-\beta A_\star(z,\beta)\bigr)dz$, resp. $dz$. Thus the dynamics in~\eqref{eq:bias_simple} reaches asymptotically a {\it flat histogram} property in the $z=\xi(x)$ direction; the exploration of $\mathbb{T}^m$ is thus faster for $\xi(X^\star)$ than for $\xi(X^0)$, and in turn the convergence of $X^\star$ to $\mu_{\beta}^{\star}$ is expected to be faster than the convergence of $X^0$ to $\mu_\beta$.

Finally, the construction of the ABP method~\eqref{eq:ABP_simple}, in particular the use of
{\it weighted} empirical distributions $\overline{\mu}_t$, is motivated by the following almost sure convergence: for any continuous $\varphi:\mathbb{T}^d\to \mathbb{R}$,
\begin{equation}\label{eq:identity_bias-unbiased_simple}
\frac{\frac{1}{t}\int_{0}^{t}\exp\bigl(-\beta A_\star(\xi(X_r^\star),\beta)\bigr)\varphi(X_r^\star)dr}{\frac{1}{t}\int_{0}^{t}\exp\bigl(-\beta A_\star(\xi(X_r^\star),\beta)\bigr)dr}\underset{t\to +\infty}\to\mu_{\beta}^{\star}\bigl(\varphi \exp\bigl(-\beta A_{\star}(\xi(\cdot),\beta)\bigr)\bigr)=\mu_{\beta}(\varphi).
\end{equation}
Theorem~\ref{th:cv_mu} thus extends this consistency property from a non-adaptive \eqref{eq:bias_simple} to an adaptive dynamics~\eqref{eq:ABP_simple}.

\section{Proof of Theorem~\ref{th:cv_mu}}\label{sec:ABP}

In this section, we provide the main ideas of the proof of Theorem~\ref{th:cv_mu}.Some technical arguments are skipped, and will be fully detailed in~\cite{BenaimBrehier}, in a more general framework. We first state an important property of $A_t$, and then introduce a change of variables, which helps us identifying a more standard form for self-interacting diffusion processes. We then adapt in our context the arguments from~\cite{BenaimLedouxRaimond1}, to establish the consistency of the ABP approach thanks to the ODE method from stochastic approximation theory.

\subsection{Properties of the ABP dynamics~\eqref{eq:ABP_simple}}

Our first task in the study of the ABP dynamics is to study the well-posedness of the equation, {\it i.e.} the existence of a unique global solution $t\mapsto (X_t,\overline{\mu}_t,A_t)\in \mathbb{T}^d\times \mathcal{P}(\mathbb{T}^d)\times \mathcal{C}^\infty(\mathbb{T}^m)$. In order to apply a standard fixed point/Picard iteration strategy, it is essential to control the Lipschitz constant of $\nabla\bigl(A_t\circ\xi\bigr)$ (first equation in~\eqref{eq:ABP_simple}). This key stability property is ensured as follows. Let $m=\min_{z,\zeta\in\mathbb{T}^m}K(z,\zeta)$, and $M^{(n)}=\max_{z,\zeta}|\partial_z^{n}K(z,\zeta)|$ for $n\in\left\{0,1\right\}$, where $\partial_z^n$ denotes the differential of order $n$, and introduce
$$\mathcal{A}=\left\{A\in \mathcal{C}^{\infty}(\mathbb{T}^m)~|~ \min_{z\in\mathbb{T}^m}e^{-\beta A(z)}\ge m, \max_{z\in\mathbb{T}^m}|\partial_z^n e^{-\beta A(z)}|\le M^{(n)}, n=0,1\right\}.$$
Then $\mathcal{A}$ is  left invariant by the evolution $t\mapsto A_t$, {\it i.e.} $A_0\in\mathcal{A}$ implies $A_t\in\mathcal{A}$ for all $t\ge 0$, almost surely.

\subsection{Change of variables}

The stochastic process $t\mapsto \overline{\mu}_t$, with values in $\mathcal{P}(\mathbb{T}^d)$, is the unique solution of the random Ordinary Differential Equation (ODE), interpreted in a weak sense (considering continuous bounded test functions):
\begin{equation}\label{eq:ODE_mu}
\frac{d\overline{\mu}_t}{dt}=\frac{\theta'(t)}{1+\theta(t)}\bigl(\delta_{X_t}-\overline{\mu}_t\bigr),
\end{equation}
where $\theta(t)=\int_{0}^{t}\exp\bigl(-\beta A_r(\xi(X_r))\bigr)dr$.
The random function $\theta:[0,+\infty)\to [0,+\infty)$ is a $\mathcal{C}^1$-diffeomorphism: indeed for all $t\ge 0$, almost surely $\theta'(t)=\exp\bigl(-\beta A_t(\xi(X_t))\bigr)\in[m,M]$. This fundamental property allows us to apply the following change of variables
\begin{equation}\label{eq:change}
s=\theta(t) \quad,\quad t=\theta^{-1}(s) \quad;\quad Y_s=X_t \quad,\quad \overline{\nu}_s=\overline{\mu}_t \quad,\quad B_s=A_t.
\end{equation}
Observe that $s=\theta(t)\underset{t\to +\infty}\to +\infty$ and that $t=\theta^{-1}(s)\underset{s\to +\infty}\to +\infty$, almost surely. Instead of studying the asymptotic behavior of $\overline{\mu}_t$ when $t\to +\infty$, it thus equivalent to study the asymptotic behavior of $\overline{\nu}_s$ when $s\to +\infty$. In the new variables~\eqref{eq:change}, the ABP dynamics~\eqref{eq:ABP_simple} writes
\begin{equation}\label{eq:ABP_simple_s}
\begin{cases}
dY_s=-\nabla\bigl(V-B_s\circ \xi\bigr)(Y_s)e^{\beta B_s(\xi(Y_s))}ds+\sqrt{2\beta^{-1}e^{\beta B_s(\xi(Y_s))}}d\tilde{W}(s)\\
\overline{\nu}_s=\frac{\overline{\nu}_0+\int_{0}^{s}\delta_{Y_r}dr}{1+s}\\
\exp\bigl(-\beta B_s(z)\bigr)=\int_{\mathbb{T}^d}K(z,\xi(x))\overline{\nu}_s(dx),
\end{cases}
\end{equation}
where $\tilde{W}$ is a new standard Brownian motion on $\mathbb{T}^d$, defined from $W$ and $\theta$. Notice that $\overline{\nu}_s$ is a {\it nonweighted empirical distribution} and that $s\mapsto \overline{\nu}_s$ satisfies the simpler random ODE
\begin{equation}\label{eq:ODE_nu}
\frac{d\overline{\nu}_s}{ds}=\frac{1}{1+s}\bigl(\delta_{Y_s}-\overline{\nu}_s\bigr).
\end{equation}
The change of variable~\eqref{eq:change} both removes $\theta(t)$ from~\eqref{eq:ODE_mu} as well as the weigths $\exp\bigl(-\beta A_t(\xi(X_t))\bigr)=\theta'(t)$ from~\eqref{eq:ABP_simple}.

Thanks to Equation~\eqref{eq:ABP_simple_s}, an analogy with the framework of~\cite{BenaimLedouxRaimond1} can now be made. Even though we cannot directly apply the results therein, due to the specific form of the dynamics on $Y$, we follow the same strategy for the analysis of $\overline{\nu}_s$ when $s\to +\infty$: we use the {\it ODE method}.

\subsection{Application of the ODE method and sketch of proof of Theorem~\ref{th:cv_mu}}

The guideline of the so-called ODE approach we wish to apply is as follows: there is an asymptotic time-scale separation between the (fast) evolution of $Y_s$ and the (slow) evolution of $\overline{\nu}_s$ (and of $B_s$). The asymptotic behavior of $\overline{\nu}_s$ is then determined by a so-called limit ODE, where $\delta_{Y_s}$ is replaced in~\eqref{eq:ODE_nu} with the unique invariant probability distribution of the following SDE on $\mathbb{T}^d$,
\begin{equation}\label{eq:Y_frozen_simple}
dY_s^B=-\nabla\bigl(V-B\circ \xi\bigr)(Y_s)e^{\beta B(\xi(Y_s))}ds+\sqrt{2\beta^{-1}e^{\beta B(\xi(Y_s))}}d\tilde{W}(s),
\end{equation}
{\it i.e.} the first (fast) equation of~\eqref{eq:ABP_simple_s} where the slowly varying variable $B_s$ is frozen at an arbitrary $B\in\mathcal{A}$. In fact, we have the following fundamental result: the invariant distribution of~\eqref{eq:Y_frozen_simple} does not depend on $B$.
\begin{proposition}\label{propo:consis}
For any smooth $B:\mathbb{T}^m\to \mathbb{R}$, the unique invariant distribution of~\eqref{eq:Y_frozen_simple} is $\mu_\beta$.
\end{proposition}
Proposition~\ref{propo:consis} is essential and its proof is very simple. Indeed, introduce the generator $\mathcal{L}_X^B$ of $X^B$, resp. the unique invariant distribution of $X^B$, denoted by $\mu_\beta^B(dx)=Z^B(\beta)^{-1}\exp\bigl(-\beta (V-B\circ \xi)(x)\bigr)dx$, with the diffusion
$dX_t^B=-\nabla\bigl(V-B\circ \xi\bigr)(Y_s)dt+\sqrt{2\beta^{-1}}dW(t)$.
Then the generator $\mathcal{L}_Y^B$ of $Y^B$ defined by~\eqref{eq:Y_frozen_simple} is equal to $\exp\bigl(\beta B\circ\xi\bigr)\mathcal{L}_X^B$. Proposition~\ref{propo:consis} is a consequence of the following identity: for any smooth $\phi,\psi:\mathbb{T}^d\to \mathbb{R}$,
$$\int_{\mathbb{T}^d}\phi(y)\mathcal{L}_Y^B\psi(y)\mu_\beta(dy)
=\int_{\mathbb{T}^d}\phi(x)\mathcal{L}_X^B\psi(x)\mu_\beta^B(dx)=0.$$

We now outline the end of the proof of Theorem~\ref{th:cv_mu}, adapting the arguments from~\cite{BenaimLedouxRaimond1} in our original case; details in a more general setting are given in~\cite{BenaimBrehier}. The ODE method suggests us to define $\Gamma(\sigma,s,\nu)=\Gamma_{\sigma-s}(\nu)$, for any $\sigma\ge s$ and $\nu\in\mathcal{P}(\mathbb{T}^d)$, where $\Gamma_s(\nu)=e^{-s}\nu+(1-e^{-s})\mu_\beta\underset{s\to +\infty}\to\mu_\beta$ is the solution of $\frac{d\Gamma_s}{ds}=\mu_\beta-\Gamma_s$ with $\Gamma_0(\nu)=\nu$.
To state (without proof) our last techincal result, we recall that weak convergence in $\mathcal{P}(\mathbb{T}^d)$ is associated with the following metric
$$d\bigl(\mu^1,\mu^2\bigr)=\sum_{n=1}^{+\infty}\frac{1}{2^n}\min\bigl(1,|\int_{\mathbb{T}^d}f_nd\mu^1-f_nd\mu^2|\bigr),$$
for a given family $\bigl(f_n\bigr)_{n\ge 1}$ of $\mathcal{C}^\infty$ functions, which is dense in $\mathcal{C}^0(\mathbb{T}^d)$

\begin{proposition}\label{propo:APT}
For any $S\ge 0$, almost surely
$$\Delta(s,S)=\sup_{\sigma\in[0,S]} d\bigl(\overline{\nu}_{\exp(s+\sigma)},\Gamma(\sigma,s,\overline{\nu}_s)\bigr)\underset{s\to +\infty}\to 0,$$
{\it i.e.} almost surely $s\mapsto \overline{\nu}_s$ is an {\it asymptotic pseudo-trajectory} of the semi-flow~$\Gamma$.
\end{proposition}
We refer to~\cite{BenaimLedouxRaimond1} for a proof of a similar result in a different context, and to~\cite{BenaimBrehier} for a detailed proof in a more general context; the main difference between the two situations is the use of a specific Poisson equation related to the generator of~\eqref{eq:Y_frozen_simple}.

To conclude, observe that $d\bigl(\overline{\nu}_{\exp(s)},\mu_{\beta}\bigr)\leq \Delta(s-S,S)+d\bigl(\Gamma_{S}(\overline{\nu}_{\exp(s)}),\mu_\beta\bigr)$. Letting first $s$, then $S$, go to $+\infty$, Proposition~\ref{propo:APT} implies the main result of this paper, Theorem~\ref{th:cv_mu}.

\section*{Acknowledgements}

The authors would like to thank Tony Leli\`evre and Gabriel Stoltz for helpful comments. The work is partially supported by the Swiss National Foundation, Grants: $200020 \_ 149871$ and $200021 \_ 163072$.

redpajama_set_name: RedPajamaArXiv


text:
Q: Problem with variadic template expansion in Visual Studio This code works nicely with gcc:
#include <iostream>
#include <type_traits>
#include <utility>

template <bool... Bs>
struct bool_sequence {};

template <bool... Bs>
using bool_and = std::is_same<
                            bool_sequence<Bs...>,
                            bool_sequence<(Bs || true)...>
                            >;
template <bool... Bs>
using bool_or = std::integral_constant<bool, !bool_and<!Bs...>::value>;

int main(int argc, char* argv[])
{
    std::cout << bool_or<true>::value << std::endl;
    std::cout << bool_or<true, true>::value << std::endl;
    std::cout << bool_or<true, true, true>::value << std::endl;
}

Expected output: 1 1 1.
Here live example
But  VS 2017 outputs: 0 0 0.
Is this a bug in VS or am I missing something here ?
Edit:  VS 2017, v141, cl: 19.16.27030.1
Thanks

A: This doesnt answer my question directly, but is just a workaround (actually not really workaround, but much cleaner solution for the real code comparing to the MVCE above) using std::conjunction/disjunction as propoesed by @Frank in the comment, for the case that someone else lands here for the same reason.
This works on VS as expected:
#include <iostream>
#include <type_traits>
#include <utility>

template <bool... Bs>
using bool_and =
    std::conjunction<std::integral_constant<bool, Bs>...>;

template <bool... Bs>
using bool_or =
    std::disjunction<std::integral_constant<bool, Bs>...>;

int main()
{
    std::cout << bool_or<true>::value << std::endl;
    std::cout << bool_or<true, true>::value << std::endl;
    std::cout << bool_or<true, true, true>::value << std::endl;
}

and also live

A: Why not using c++17 fold expression:
#include <iostream>
#include <type_traits>

template <bool... Bs>
using bool_and = std::bool_constant<(Bs && ...)>;

template <bool... Bs>
using bool_or = std::bool_constant<(Bs || ...)>;

int main()
{
    std::cout << bool_or<true>::value << std::endl;
    std::cout << bool_or<false, false>::value << std::endl;
    std::cout << bool_and<true, false, true>::value << std::endl;
}

redpajama_set_name: RedPajamaStackExchange


I took VitaPulse for one year. My cholesterol went from 210 to 180, and my LDL and HDL numbers improved as well. I found another version of this made by Solar Ray with the same formulation for half the price.
I am Veronica with Princeton Nutrients. Thank you for taking the time to leave us a review. We are glad to hear that you have seen an improvement in your health since taking VitaPulse. I also want to mention that our products are made with the highest quality ingredients so that is why they are priced this way. We highly recommend you speak to your primary physician before switching to a new product. If you have any questions please reach out to me at Veronica@PrincetonNutrients.com.


One of the best lunches I had in recent months was with Carmen Popescu, Senior Project Coordinator of Pharmaceutical Applications at Roquette America. Our conversation ranged from linguistics to Ceaușescu to tabbouleh to the state of higher education in America to hair care products. Carmen is energetic, witty, and warm, the kind of person you want to spend time with. She's very down to earth, but she's also the kind of person who sees the science in, under, around, and behind everything. In other words, she's like me and just about everyone I know, except that she's a genius in pharmaceutical formulation and applications. She's the epitome of a Science Person.
In B2B marketing, most companies either are experts in their fields or claim to be one. In the B2B world, just about every company boasts innovation and proprietary solutions and technologies that differentiate them. In the race, though, to out-innovate, out-solve, and out-offer, we often lose sight of the fact that the ones innovating, solving, and offering solutions are people with everyday interests and common hobbies, people who like goofy sitcoms, weekend sports, and outlet malls. It's easy to forget that the desire to work with people we like and share interests with can far outweigh whatever features and benefits we might like in a company's product line or service offering. When it comes down to it, where the innovation, products, and services aren't largely differentiated, it's the quality of the people that makes the sale.
When we began a partnership with Roquette America, I was struck by how warm and witty and enjoyable their people are. They dissolved my uninformed notion of science experts as, well, a bit unapproachable. In fact, one of my very first discussions with one of Roquette's science experts was about Paula Deen Riding Things. It was at that moment that I knew that we had to make sure that who Roquette's science experts are as people doesn't get lost among their product and service offerings, no matter how great and effective they are (and they are pretty amazing).
That's where the Science People campaign (and the trade show booth collateral below) was born. That's what brought Carmen, along with several other Science People from Roquette's pharma division, to St. Louis for an in-house photo-shoot, and many enjoyable, interesting discussions and lots of laughs. If I were looking for a partner in pharmaceutical product development, I'd look no farther than Carmen, Cal, and Harshal, Roquette Pharma's Science People, the kinds of people anyone would enjoy working alongside.


a healthy snacks review: can I just have chocolate instead? – british. foodie. dreamer.
As I'm also starting my fitness journey to be a gym bunny (haha I can't believe I just called myself that… #dontjudgeme) and am trying to eat healthier! So, I recently purchased three different types of healthy snacks to see whether any tickle my fancy and have the best health benefits possible from a little snack bar.
My reviews work like this, I mark the Flavour, Appearance and Texture a score out of 10 and talk about each one. Let's get started! (I am not ordering them in terms of best on but the chronological order).
Trek Cocoa Oat Flapjack – review!
Maybe I loved this because I was starving having just done a workout but I am happy to say I do recommend this bar, not only is it healthy, but it does have 9g of protein which gives an extra boost to anyone who is exercising regularly or need an extra boost with what they eat. The texture was soft but not sticky like a squares bar (which I know is made with marshmallow but I hate it when stuff sticks to my teeth) and the layer of cocoa dark chocolate is not thick and only covers one side. It isn't too sweet either as the flavour of the dark chocolate balances with the sugar but also compliments the wholesome oats to satisfy your need for a snack. I could eat more, but I think one a day is perfect as I think two could be overkill. So, pretty happy to buy this one again!
Other flavours: banana bread, cocoa coconut, morning berry.
Price: in local supermarkets average £0.90 per bar, so bulk buying on amazon or other online retailers is usually a little cheaper.
I heard of this lovely lady through my mum at the beginning of the year as she also does recipes for meals and healthier options that we can cook at home! One of the dishes, which I have made since is the apple crumble. This isn't the normal dessert you expect, in fact, it's a breakfast option that you can make at the beginning of the week and just devour for breakfast with any yoghurt or milk of your choice! Recipe here!
Anyway, back to the protein ball… The appearance wasn't anything spectacular or something that I wanted to gobble up upon sight of it, nevertheless, don't just a book by its cover. The texture is quite chewy and somewhat moist because it is made with dates and roasted nut butter (as well as other ingredients) to bind it. The flavour isn't as inspiring or as yummy to the taste buds as I'd hoped as I can be quite picky about wanting a dominant flavour. It is a great snack for those who don't like sweet and sugary things as it is definitely a perfect size to satisfy your snacking needs and hunger!
Other flavours available include almond and blueberry protein ball, hazelnut and raisin energy ball, coconut and oat energy ball.
Any recommendations of other healthy snacks, energy bars or other healthy foods are most welcome as I love tasting the food and blogging about it is double the fun!
It's definitely more affordable to make the energy balls at home, as well as various other healthy snacks. If you fancy sate-ing your sweet tooth, using honey or other natural sweet ingredients are better than milk chocolate or sugar! Alternatively, as my godmother has suggested, throw together some nuts, dried fruit and dark chocolate and you're good to go! Hehe!
Posted on May 19, 2017 May 19, 2017 by GeorgiePosted in F I T N E S S & F O O D I ETagged BBG, chocolate, energy, energy bars, fitness, fitness journey, foodie, georgetta loretta, get healthy, healthy, healthy happiness, healthy snacks, protein bars.